[{"citation":{"chicago":"Fischer, Julian L, Katharina Hopf, Michael Kniely, and Alexander Mielke. “Global Existence Analysis of Energy-Reaction-Diffusion Systems.” SIAM Journal on Mathematical Analysis. Society for Industrial and Applied Mathematics, 2022. https://doi.org/10.1137/20M1387237.","ama":"Fischer JL, Hopf K, Kniely M, Mielke A. Global existence analysis of energy-reaction-diffusion systems. SIAM Journal on Mathematical Analysis. 2022;54(1):220-267. doi:10.1137/20M1387237","apa":"Fischer, J. L., Hopf, K., Kniely, M., & Mielke, A. (2022). Global existence analysis of energy-reaction-diffusion systems. SIAM Journal on Mathematical Analysis. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/20M1387237","mla":"Fischer, Julian L., et al. “Global Existence Analysis of Energy-Reaction-Diffusion Systems.” SIAM Journal on Mathematical Analysis, vol. 54, no. 1, Society for Industrial and Applied Mathematics, 2022, pp. 220–67, doi:10.1137/20M1387237.","ieee":"J. L. Fischer, K. Hopf, M. Kniely, and A. Mielke, “Global existence analysis of energy-reaction-diffusion systems,” SIAM Journal on Mathematical Analysis, vol. 54, no. 1. Society for Industrial and Applied Mathematics, pp. 220–267, 2022.","ista":"Fischer JL, Hopf K, Kniely M, Mielke A. 2022. Global existence analysis of energy-reaction-diffusion systems. SIAM Journal on Mathematical Analysis. 54(1), 220–267.","short":"J.L. Fischer, K. Hopf, M. Kniely, A. Mielke, SIAM Journal on Mathematical Analysis 54 (2022) 220–267."},"quality_controlled":"1","volume":54,"doi":"10.1137/20M1387237","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","scopus_import":"1","isi":1,"article_processing_charge":"No","day":"04","date_created":"2021-12-16T12:08:56Z","language":[{"iso":"eng"}],"author":[{"first_name":"Julian L","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","last_name":"Fischer","orcid":"0000-0002-0479-558X","full_name":"Fischer, Julian L"},{"full_name":"Hopf, Katharina","first_name":"Katharina","last_name":"Hopf"},{"orcid":"0000-0001-5645-4333","full_name":"Kniely, Michael","first_name":"Michael","id":"2CA2C08C-F248-11E8-B48F-1D18A9856A87","last_name":"Kniely"},{"last_name":"Mielke","first_name":"Alexander","full_name":"Mielke, Alexander"}],"acknowledgement":"M.K. gratefully acknowledges the hospitality of WIAS Berlin, where a major part of the project was carried out. The research stay of M.K. at WIAS Berlin was funded by the Austrian Federal Ministry of Education, Science and Research through a research fellowship for graduates of a promotio sub auspiciis. The research of A.M. has been partially supported by Deutsche Forschungsgemeinschaft (DFG) through the Collaborative Research Center SFB 1114 “Scaling Cascades in Complex Systems” (Project no. 235221301), Subproject C05 “Effective models for materials and interfaces with multiple scales”. J.F. and A.M. are grateful for the hospitality of the Erwin Schrödinger Institute in Vienna, where some ideas for this work have been developed. The authors are grateful to two anonymous referees for several helpful comments, in particular for the short proof of estimate (2.7).","article_type":"original","date_updated":"2023-08-02T13:37:03Z","issue":"1","type":"journal_article","department":[{"_id":"JuFi"}],"status":"public","page":"220-267","date_published":"2022-01-04T00:00:00Z","month":"01","publication":"SIAM Journal on Mathematical Analysis","publisher":"Society for Industrial and Applied Mathematics","publication_identifier":{"issn":["0036-1410"]},"external_id":{"isi":["000762768000006"],"arxiv":["2012.03792 "]},"arxiv":1,"year":"2022","abstract":[{"lang":"eng","text":"We establish global-in-time existence results for thermodynamically consistent reaction-(cross-)diffusion systems coupled to an equation describing heat transfer. Our main interest is to model species-dependent diffusivities,\r\nwhile at the same time ensuring thermodynamic consistency. A key difficulty of the non-isothermal case lies in the intrinsic presence of cross-diffusion type phenomena like the Soret and the Dufour effect: due to the temperature/energy dependence of the thermodynamic equilibria, a nonvanishing temperature gradient may drive a concentration flux even in a situation with constant concentrations; likewise, a nonvanishing concentration gradient may drive a heat flux even in a case of spatially constant temperature. We use time discretisation and regularisation techniques and derive a priori estimates based on a suitable entropy and the associated entropy production. Renormalised solutions are used in cases where non-integrable diffusion fluxes or reaction terms appear."}],"keyword":["Energy-Reaction-Diffusion Systems","Cross Diffusion","Global-In-Time Existence of Weak/Renormalised Solutions","Entropy Method","Onsager System","Soret/Dufour Effect"],"main_file_link":[{"url":"https://arxiv.org/abs/2012.03792","open_access":"1"}],"publication_status":"published","_id":"10547","title":"Global existence analysis of energy-reaction-diffusion systems","oa_version":"Preprint","intvolume":" 54","oa":1},{"arxiv":1,"year":"2022","abstract":[{"text":"Consider a linear elliptic partial differential equation in divergence form with a random coefficient field. The solution operator displays fluctuations around its expectation. The recently developed pathwise theory of fluctuations in stochastic homogenization reduces the characterization of these fluctuations to those of the so-called standard homogenization commutator. In this contribution, we investigate the scaling limit of this key quantity: starting\r\nfrom a Gaussian-like coefficient field with possibly strong correlations, we establish the convergence of the rescaled commutator to a fractional Gaussian field, depending on the decay of correlations of the coefficient field, and we\r\ninvestigate the (non)degeneracy of the limit. This extends to general dimension $d\\ge1$ previous results so far limited to dimension $d=1$, and to the continuum setting with strong correlations recent results in the discrete iid case.","lang":"eng"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1910.04088"}],"publication_status":"published","_id":"10548","title":"Scaling limit of the homogenization commutator for Gaussian coefficient fields","oa_version":"Preprint","intvolume":" 32","oa":1,"publisher":"Institute of Mathematical Statistics","publication_identifier":{"issn":["1050-5164"]},"external_id":{"isi":["000791003700011"],"arxiv":["1910.04088"]},"day":"28","language":[{"iso":"eng"}],"date_created":"2021-12-16T12:10:16Z","author":[{"full_name":"Duerinckx, Mitia","last_name":"Duerinckx","first_name":"Mitia"},{"first_name":"Julian L","last_name":"Fischer","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0479-558X","full_name":"Fischer, Julian L"},{"last_name":"Gloria","first_name":"Antoine","full_name":"Gloria, Antoine"}],"corr_author":"1","article_type":"original","acknowledgement":"The authors thank Ivan Nourdin and Felix Otto for inspiring discussions. The work of MD is financially supported by the CNRS-Momentum program. Financial support of AG is acknowledged from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2014-2019 Grant Agreement QUANTHOM 335410).","date_updated":"2026-08-12T09:22:31Z","issue":"2","type":"journal_article","department":[{"_id":"JuFi"}],"status":"public","page":"1179-1209","date_published":"2022-04-28T00:00:00Z","month":"04","publication":"Annals of Applied Probability","quality_controlled":"1","citation":{"short":"M. Duerinckx, J.L. Fischer, A. Gloria, Annals of Applied Probability 32 (2022) 1179–1209.","ista":"Duerinckx M, Fischer JL, Gloria A. 2022. Scaling limit of the homogenization commutator for Gaussian coefficient fields. Annals of Applied Probability. 32(2), 1179–1209.","ieee":"M. Duerinckx, J. L. Fischer, and A. Gloria, “Scaling limit of the homogenization commutator for Gaussian coefficient fields,” Annals of Applied Probability, vol. 32, no. 2. Institute of Mathematical Statistics, pp. 1179–1209, 2022.","ama":"Duerinckx M, Fischer JL, Gloria A. Scaling limit of the homogenization commutator for Gaussian coefficient fields. Annals of Applied Probability. 2022;32(2):1179-1209. doi:10.1214/21-AAP1705","apa":"Duerinckx, M., Fischer, J. L., & Gloria, A. (2022). Scaling limit of the homogenization commutator for Gaussian coefficient fields. Annals of Applied Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/21-AAP1705","mla":"Duerinckx, Mitia, et al. “Scaling Limit of the Homogenization Commutator for Gaussian Coefficient Fields.” Annals of Applied Probability, vol. 32, no. 2, Institute of Mathematical Statistics, 2022, pp. 1179–209, doi:10.1214/21-AAP1705.","chicago":"Duerinckx, Mitia, Julian L Fischer, and Antoine Gloria. “Scaling Limit of the Homogenization Commutator for Gaussian Coefficient Fields.” Annals of Applied Probability. Institute of Mathematical Statistics, 2022. https://doi.org/10.1214/21-AAP1705."},"volume":32,"doi":"10.1214/21-AAP1705","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","scopus_import":"1","isi":1,"article_processing_charge":"No"},{"external_id":{"arxiv":["2203.17143"]},"article_processing_charge":"No","project":[{"call_identifier":"H2020","grant_number":"948819","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","name":"Bridging Scales in Random Materials"}],"doi":"10.48550/ARXIV.2203.17143","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"chicago":"Fischer, Julian L, and Alice Marveggio. “Quantitative Convergence of the Vectorial Allen-Cahn Equation towards Multiphase Mean Curvature Flow.” ArXiv, n.d. https://doi.org/10.48550/ARXIV.2203.17143.","mla":"Fischer, Julian L., and Alice Marveggio. “Quantitative Convergence of the Vectorial Allen-Cahn Equation towards Multiphase Mean Curvature Flow.” ArXiv, 2203.17143, doi:10.48550/ARXIV.2203.17143.","ama":"Fischer JL, Marveggio A. Quantitative convergence of the vectorial Allen-Cahn equation towards multiphase mean curvature flow. arXiv. doi:10.48550/ARXIV.2203.17143","apa":"Fischer, J. L., & Marveggio, A. (n.d.). Quantitative convergence of the vectorial Allen-Cahn equation towards multiphase mean curvature flow. arXiv. https://doi.org/10.48550/ARXIV.2203.17143","ieee":"J. L. Fischer and A. Marveggio, “Quantitative convergence of the vectorial Allen-Cahn equation towards multiphase mean curvature flow,” arXiv. .","ista":"Fischer JL, Marveggio A. Quantitative convergence of the vectorial Allen-Cahn equation towards multiphase mean curvature flow. arXiv, 2203.17143.","short":"J.L. Fischer, A. Marveggio, ArXiv (n.d.)."},"article_number":"2203.17143","date_published":"2022-03-31T00:00:00Z","month":"03","oa":1,"ec_funded":1,"publication":"arXiv","status":"public","type":"preprint","oa_version":"Preprint","department":[{"_id":"JuFi"}],"_id":"14597","publication_status":"draft","date_updated":"2026-08-12T09:15:49Z","title":"Quantitative convergence of the vectorial Allen-Cahn equation towards multiphase mean curvature flow","related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"14587"},{"relation":"later_version","id":"17481","status":"public"}]},"main_file_link":[{"url":"https://arxiv.org/abs/2203.17143","open_access":"1"}],"year":"2022","abstract":[{"text":"Phase-field models such as the Allen-Cahn equation may give rise to the formation and evolution of geometric shapes, a phenomenon that may be analyzed rigorously in suitable scaling regimes. In its sharp-interface limit, the vectorial Allen-Cahn equation with a potential with N≥3 distinct minima has been conjectured to describe the evolution of branched interfaces by multiphase mean curvature flow.\r\nIn the present work, we give a rigorous proof for this statement in two and three ambient dimensions and for a suitable class of potentials: As long as a strong solution to multiphase mean curvature flow exists, solutions to the vectorial Allen-Cahn equation with well-prepared initial data converge towards multiphase mean curvature flow in the limit of vanishing interface width parameter ε↘0. We even establish the rate of convergence O(ε1/2).\r\nOur approach is based on the gradient flow structure of the Allen-Cahn equation and its limiting motion: Building on the recent concept of \"gradient flow calibrations\" for multiphase mean curvature flow, we introduce a notion of relative entropy for the vectorial Allen-Cahn equation with multi-well potential. This enables us to overcome the limitations of other approaches, e.g. avoiding the need for a stability analysis of the Allen-Cahn operator or additional convergence hypotheses for the energy at positive times.","lang":"eng"}],"corr_author":"1","author":[{"full_name":"Fischer, Julian L","orcid":"0000-0002-0479-558X","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","last_name":"Fischer","first_name":"Julian L"},{"full_name":"Marveggio, Alice","first_name":"Alice","id":"25647992-AA84-11E9-9D75-8427E6697425","last_name":"Marveggio"}],"arxiv":1,"language":[{"iso":"eng"}],"day":"31","date_created":"2023-11-23T09:30:02Z"},{"abstract":[{"lang":"eng","text":"The present thesis is concerned with the derivation of weak-strong uniqueness principles for curvature driven interface evolution problems not satisfying a comparison principle. The specific examples being treated are two-phase Navier-Stokes flow with surface tension, modeling the evolution of two incompressible, viscous and immiscible fluids separated by a sharp interface, and multiphase mean curvature flow, which serves as an idealized model for the motion of grain boundaries in an annealing polycrystalline material. Our main results - obtained in joint works with Julian Fischer, Tim Laux and Theresa M. Simon - state that prior to the formation of geometric singularities due to topology changes, the weak solution concept of Abels (Interfaces Free Bound. 9, 2007) to two-phase Navier-Stokes flow with surface tension and the weak solution concept of Laux and Otto (Calc. Var. Partial Differential Equations 55, 2016) to multiphase mean curvature flow (for networks in R^2 or double bubbles in R^3) represents the unique solution to these interface evolution problems within the class of classical solutions, respectively. To the best of the author's knowledge, for interface evolution problems not admitting a geometric comparison principle the derivation of a weak-strong uniqueness principle represented an open problem, so that the works contained in the present thesis constitute the first positive results in this direction. The key ingredient of our approach consists of the introduction of a novel concept of relative entropies for a class of curvature driven interface evolution problems, for which the associated energy contains an interfacial contribution being proportional to the surface area of the evolving (network of) interface(s). The interfacial part of the relative entropy gives sufficient control on the interface error between a weak and a classical solution, and its time evolution can be computed, at least in principle, for any energy dissipating weak solution concept. A resulting stability estimate for the relative entropy essentially entails the above mentioned weak-strong uniqueness principles. The present thesis contains a detailed introduction to our relative entropy approach, which in particular highlights potential applications to other problems in curvature driven interface evolution not treated in this thesis."}],"year":"2021","ec_funded":1,"oa":1,"oa_version":"Published Version","title":"Curvature driven interface evolution: Uniqueness properties of weak solution concepts","_id":"10007","publication_status":"published","publisher":"Institute of Science and Technology Austria","supervisor":[{"id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","last_name":"Fischer","first_name":"Julian L","full_name":"Fischer, Julian L","orcid":"0000-0002-0479-558X"}],"alternative_title":["ISTA Thesis"],"publication_identifier":{"issn":["2663-337X"]},"project":[{"call_identifier":"H2020","grant_number":"665385","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","name":"International IST Doctoral Program"},{"_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","name":"Bridging Scales in Random Materials","call_identifier":"H2020","grant_number":"948819"}],"OA_place":"publisher","related_material":{"record":[{"id":"10012","status":"public","relation":"part_of_dissertation"},{"id":"10013","status":"public","relation":"part_of_dissertation"},{"id":"7489","status":"public","relation":"part_of_dissertation"}]},"corr_author":"1","author":[{"full_name":"Hensel, Sebastian","orcid":"0000-0001-7252-8072","last_name":"Hensel","id":"4D23B7DA-F248-11E8-B48F-1D18A9856A87","first_name":"Sebastian"}],"file_date_updated":"2021-09-15T14:37:30Z","day":"14","language":[{"iso":"eng"}],"date_created":"2021-09-13T11:12:34Z","ddc":["515"],"month":"09","date_published":"2021-09-14T00:00:00Z","page":"300","status":"public","has_accepted_license":"1","department":[{"_id":"GradSch"},{"_id":"JuFi"}],"type":"dissertation","degree_awarded":"PhD","date_updated":"2026-04-08T07:01:01Z","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","doi":"10.15479/at:ista:10007","citation":{"apa":"Hensel, S. (2021). Curvature driven interface evolution: Uniqueness properties of weak solution concepts. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:10007","ama":"Hensel S. Curvature driven interface evolution: Uniqueness properties of weak solution concepts. 2021. doi:10.15479/at:ista:10007","mla":"Hensel, Sebastian. Curvature Driven Interface Evolution: Uniqueness Properties of Weak Solution Concepts. Institute of Science and Technology Austria, 2021, doi:10.15479/at:ista:10007.","chicago":"Hensel, Sebastian. “Curvature Driven Interface Evolution: Uniqueness Properties of Weak Solution Concepts.” Institute of Science and Technology Austria, 2021. https://doi.org/10.15479/at:ista:10007.","ista":"Hensel S. 2021. Curvature driven interface evolution: Uniqueness properties of weak solution concepts. Institute of Science and Technology Austria.","short":"S. Hensel, Curvature Driven Interface Evolution: Uniqueness Properties of Weak Solution Concepts, Institute of Science and Technology Austria, 2021.","ieee":"S. Hensel, “Curvature driven interface evolution: Uniqueness properties of weak solution concepts,” Institute of Science and Technology Austria, 2021."},"article_processing_charge":"No","file":[{"creator":"shensel","checksum":"c8475faaf0b680b4971f638f1db16347","date_updated":"2021-09-15T14:37:30Z","file_id":"10008","file_size":15022154,"content_type":"application/x-zip-compressed","date_created":"2021-09-13T11:03:24Z","access_level":"closed","relation":"source_file","file_name":"thesis_final_Hensel.zip"},{"file_name":"thesis_final_Hensel.pdf","relation":"main_file","date_created":"2021-09-13T14:18:56Z","access_level":"open_access","content_type":"application/pdf","file_size":6583638,"file_id":"10014","date_updated":"2021-09-14T09:52:47Z","checksum":"1a609937aa5275452822f45f2da17f07","creator":"shensel"}]},{"article_number":"2108.01733","external_id":{"arxiv":["2108.01733"]},"project":[{"_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","name":"Bridging Scales in Random Materials","call_identifier":"H2020","grant_number":"948819"}],"main_file_link":[{"url":"https://arxiv.org/abs/2108.01733","open_access":"1"}],"year":"2021","abstract":[{"lang":"eng","text":"We derive a weak-strong uniqueness principle for BV solutions to multiphase mean curvature flow of triple line clusters in three dimensions. Our proof is based on the explicit construction of a gradient-flow calibration in the sense of the recent work of Fischer et al. [arXiv:2003.05478] for any such cluster. This extends the two-dimensional construction to the three-dimensional case of surfaces meeting along triple junctions."}],"arxiv":1,"ec_funded":1,"oa":1,"oa_version":"Preprint","publication_status":"draft","_id":"10013","title":"Weak-strong uniqueness for the mean curvature flow of double bubbles","doi":"10.48550/arXiv.2108.01733","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Hensel S, Laux T. Weak-strong uniqueness for the mean curvature flow of double bubbles. arXiv, 2108.01733.","short":"S. Hensel, T. Laux, ArXiv (n.d.).","ieee":"S. Hensel and T. Laux, “Weak-strong uniqueness for the mean curvature flow of double bubbles,” arXiv. .","apa":"Hensel, S., & Laux, T. (n.d.). Weak-strong uniqueness for the mean curvature flow of double bubbles. arXiv. https://doi.org/10.48550/arXiv.2108.01733","ama":"Hensel S, Laux T. Weak-strong uniqueness for the mean curvature flow of double bubbles. arXiv. doi:10.48550/arXiv.2108.01733","mla":"Hensel, Sebastian, and Tim Laux. “Weak-Strong Uniqueness for the Mean Curvature Flow of Double Bubbles.” ArXiv, 2108.01733, doi:10.48550/arXiv.2108.01733.","chicago":"Hensel, Sebastian, and Tim Laux. “Weak-Strong Uniqueness for the Mean Curvature Flow of Double Bubbles.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2108.01733."},"article_processing_charge":"No","related_material":{"record":[{"relation":"later_version","id":"13043","status":"public"},{"status":"public","id":"10007","relation":"dissertation_contains"}]},"corr_author":"1","acknowledgement":"This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 948819), and from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy – EXC-2047/1 – 390685813.","author":[{"orcid":"0000-0001-7252-8072","full_name":"Hensel, Sebastian","first_name":"Sebastian","id":"4D23B7DA-F248-11E8-B48F-1D18A9856A87","last_name":"Hensel"},{"full_name":"Laux, Tim","last_name":"Laux","first_name":"Tim"}],"language":[{"iso":"eng"}],"date_created":"2021-09-13T12:17:11Z","day":"03","date_published":"2021-08-03T00:00:00Z","month":"08","publication":"arXiv","status":"public","type":"preprint","department":[{"_id":"JuFi"}],"date_updated":"2026-04-08T07:01:01Z"},{"scopus_import":"1","file":[{"success":1,"file_name":"2021_ArchRatMechAnalysis_Fischer.pdf","access_level":"open_access","date_created":"2021-12-16T14:58:08Z","relation":"main_file","file_size":1640121,"content_type":"application/pdf","file_id":"10558","date_updated":"2021-12-16T14:58:08Z","checksum":"cc830b739aed83ca2e32c4e0ce266a4c","creator":"cchlebak"}],"article_processing_charge":"Yes (via OA deal)","isi":1,"citation":{"short":"J.L. Fischer, S. Neukamm, Archive for Rational Mechanics and Analysis 242 (2021) 343–452.","ista":"Fischer JL, Neukamm S. 2021. Optimal homogenization rates in stochastic homogenization of nonlinear uniformly elliptic equations and systems. Archive for Rational Mechanics and Analysis. 242(1), 343–452.","ieee":"J. L. Fischer and S. Neukamm, “Optimal homogenization rates in stochastic homogenization of nonlinear uniformly elliptic equations and systems,” Archive for Rational Mechanics and Analysis, vol. 242, no. 1. Springer Nature, pp. 343–452, 2021.","apa":"Fischer, J. L., & Neukamm, S. (2021). Optimal homogenization rates in stochastic homogenization of nonlinear uniformly elliptic equations and systems. Archive for Rational Mechanics and Analysis. Springer Nature. https://doi.org/10.1007/s00205-021-01686-9","ama":"Fischer JL, Neukamm S. Optimal homogenization rates in stochastic homogenization of nonlinear uniformly elliptic equations and systems. Archive for Rational Mechanics and Analysis. 2021;242(1):343-452. doi:10.1007/s00205-021-01686-9","mla":"Fischer, Julian L., and Stefan Neukamm. “Optimal Homogenization Rates in Stochastic Homogenization of Nonlinear Uniformly Elliptic Equations and Systems.” Archive for Rational Mechanics and Analysis, vol. 242, no. 1, Springer Nature, 2021, pp. 343–452, doi:10.1007/s00205-021-01686-9.","chicago":"Fischer, Julian L, and Stefan Neukamm. “Optimal Homogenization Rates in Stochastic Homogenization of Nonlinear Uniformly Elliptic Equations and Systems.” Archive for Rational Mechanics and Analysis. Springer Nature, 2021. https://doi.org/10.1007/s00205-021-01686-9."},"quality_controlled":"1","volume":242,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","doi":"10.1007/s00205-021-01686-9","type":"journal_article","issue":"1","department":[{"_id":"JuFi"}],"has_accepted_license":"1","date_updated":"2023-08-17T06:23:21Z","date_published":"2021-06-30T00:00:00Z","month":"06","ddc":["530"],"publication":"Archive for Rational Mechanics and Analysis","status":"public","page":"343-452","author":[{"last_name":"Fischer","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","first_name":"Julian L","full_name":"Fischer, Julian L","orcid":"0000-0002-0479-558X"},{"full_name":"Neukamm, Stefan","first_name":"Stefan","last_name":"Neukamm"}],"language":[{"iso":"eng"}],"date_created":"2021-12-16T12:12:33Z","day":"30","file_date_updated":"2021-12-16T14:58:08Z","article_type":"original","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). SN acknowledges partial support by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – project number 405009441.","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"external_id":{"isi":["000668431200001"],"arxiv":["1908.02273"]},"publication_identifier":{"issn":["0003-9527"],"eissn":["1432-0673"]},"publisher":"Springer Nature","oa_version":"Published Version","_id":"10549","publication_status":"published","title":"Optimal homogenization rates in stochastic homogenization of nonlinear uniformly elliptic equations and systems","intvolume":" 242","oa":1,"arxiv":1,"year":"2021","keyword":["Mechanical Engineering","Mathematics (miscellaneous)","Analysis"],"abstract":[{"lang":"eng","text":"We derive optimal-order homogenization rates for random nonlinear elliptic PDEs with monotone nonlinearity in the uniformly elliptic case. More precisely, for a random monotone operator on \\mathbb {R}^d with stationary law (that is spatially homogeneous statistics) and fast decay of correlations on scales larger than the microscale \\varepsilon >0, we establish homogenization error estimates of the order \\varepsilon in case d\\geqq 3, and of the order \\varepsilon |\\log \\varepsilon |^{1/2} in case d=2. Previous results in nonlinear stochastic homogenization have been limited to a small algebraic rate of convergence \\varepsilon ^\\delta . We also establish error estimates for the approximation of the homogenized operator by the method of representative volumes of the order (L/\\varepsilon )^{-d/2} for a representative volume of size L. Our results also hold in the case of systems for which a (small-scale) C^{1,\\alpha } regularity theory is available."}]},{"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2004.02618"}],"year":"2021","abstract":[{"lang":"eng","text":"This paper is concerned with a non-isothermal Cahn-Hilliard model based on a microforce balance. The model was derived by A. Miranville and G. Schimperna starting from the two fundamental laws of Thermodynamics, following M. Gurtin's two-scale approach. The main working assumptions are made on the behaviour of the heat flux as the absolute temperature tends to zero and to infinity. A suitable Ginzburg-Landau free energy is considered. Global-in-time existence for the initial-boundary value problem associated to the entropy formulation and, in a subcase, also to the weak formulation of the model is proved by deriving suitable a priori estimates and by showing weak sequential stability of families of approximating solutions. At last, some highlights are given regarding a possible approximation scheme compatible with the a-priori estimates available for the system."}],"arxiv":1,"intvolume":" 274","oa":1,"oa_version":"Preprint","_id":"8792","publication_status":"published","title":"On a non-isothermal Cahn-Hilliard model based on a microforce balance","publisher":"Elsevier","external_id":{"arxiv":["2004.02618"],"isi":["000600845300023"]},"publication_identifier":{"issn":["0022-0396"],"eissn":["1090-2732"]},"article_type":"original","acknowledgement":"G. Schimperna has been partially supported by GNAMPA (Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni) of INdAM (Istituto Nazionale di Alta Matematica).","author":[{"full_name":"Marveggio, Alice","id":"25647992-AA84-11E9-9D75-8427E6697425","last_name":"Marveggio","first_name":"Alice"},{"last_name":"Schimperna","first_name":"Giulio","full_name":"Schimperna, Giulio"}],"date_created":"2020-11-22T23:01:26Z","language":[{"iso":"eng"}],"day":"15","month":"02","date_published":"2021-02-15T00:00:00Z","publication":"Journal of Differential Equations","status":"public","page":"924-970","issue":"2","type":"journal_article","department":[{"_id":"JuFi"}],"date_updated":"2025-07-10T12:01:25Z","doi":"10.1016/j.jde.2020.10.030","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","citation":{"mla":"Marveggio, Alice, and Giulio Schimperna. “On a Non-Isothermal Cahn-Hilliard Model Based on a Microforce Balance.” Journal of Differential Equations, vol. 274, no. 2, Elsevier, 2021, pp. 924–70, doi:10.1016/j.jde.2020.10.030.","ama":"Marveggio A, Schimperna G. On a non-isothermal Cahn-Hilliard model based on a microforce balance. Journal of Differential Equations. 2021;274(2):924-970. doi:10.1016/j.jde.2020.10.030","apa":"Marveggio, A., & Schimperna, G. (2021). On a non-isothermal Cahn-Hilliard model based on a microforce balance. Journal of Differential Equations. Elsevier. https://doi.org/10.1016/j.jde.2020.10.030","chicago":"Marveggio, Alice, and Giulio Schimperna. “On a Non-Isothermal Cahn-Hilliard Model Based on a Microforce Balance.” Journal of Differential Equations. Elsevier, 2021. https://doi.org/10.1016/j.jde.2020.10.030.","ista":"Marveggio A, Schimperna G. 2021. On a non-isothermal Cahn-Hilliard model based on a microforce balance. Journal of Differential Equations. 274(2), 924–970.","short":"A. Marveggio, G. Schimperna, Journal of Differential Equations 274 (2021) 924–970.","ieee":"A. Marveggio and G. Schimperna, “On a non-isothermal Cahn-Hilliard model based on a microforce balance,” Journal of Differential Equations, vol. 274, no. 2. Elsevier, pp. 924–970, 2021."},"volume":274,"article_processing_charge":"No","isi":1,"scopus_import":"1"},{"year":"2021","abstract":[{"text":"A stochastic PDE, describing mesoscopic fluctuations in systems of weakly interacting inertial particles of finite volume, is proposed and analysed in any finite dimension . It is a regularised and inertial version of the Dean–Kawasaki model. A high-probability well-posedness theory for this model is developed. This theory improves significantly on the spatial scaling restrictions imposed in an earlier work of the same authors, which applied only to significantly larger particles in one dimension. The well-posedness theory now applies in d-dimensions when the particle-width ϵ is proportional to for and N is the number of particles. This scaling is optimal in a certain Sobolev norm. Key tools of the analysis are fractional Sobolev spaces, sharp bounds on Bessel functions, separability of the regularisation in the d-spatial dimensions, and use of the Faà di Bruno's formula.","lang":"eng"}],"publication_status":"published","_id":"9240","title":"Well-posedness for a regularised inertial Dean–Kawasaki model for slender particles in several space dimensions","oa_version":"Published Version","intvolume":" 284","oa":1,"ec_funded":1,"publisher":"Elsevier","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"project":[{"grant_number":"754411","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships"}],"publication_identifier":{"issn":["0022-0396"],"eissn":["1090-2732"]},"external_id":{"isi":["000634823300010"]},"day":"25","date_created":"2021-03-14T23:01:32Z","language":[{"iso":"eng"}],"file_date_updated":"2021-03-22T07:18:01Z","author":[{"first_name":"Federico","id":"2CEB641C-A400-11E9-A717-D712E6697425","last_name":"Cornalba","orcid":"0000-0002-6269-5149","full_name":"Cornalba, Federico"},{"first_name":"Tony","last_name":"Shardlow","full_name":"Shardlow, Tony"},{"last_name":"Zimmer","first_name":"Johannes","full_name":"Zimmer, Johannes"}],"article_type":"original","acknowledgement":"All authors thank the anonymous referee for his/her careful reading of the manuscript and valuable suggestions. This paper was motivated by stimulating discussions at the First Berlin–Leipzig Workshop on Fluctuating Hydrodynamics in August 2019 with Ana Djurdjevac, Rupert Klein and Ralf Kornhuber. JZ gratefully acknowledges funding by a Royal Society Wolfson Research Merit Award. FC gratefully acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 754411.","date_updated":"2025-04-14T07:43:51Z","type":"journal_article","issue":"5","department":[{"_id":"JuFi"}],"has_accepted_license":"1","status":"public","page":"253-283","date_published":"2021-05-25T00:00:00Z","ddc":["510"],"month":"05","publication":"Journal of Differential Equations","quality_controlled":"1","citation":{"short":"F. Cornalba, T. Shardlow, J. Zimmer, Journal of Differential Equations 284 (2021) 253–283.","ista":"Cornalba F, Shardlow T, Zimmer J. 2021. Well-posedness for a regularised inertial Dean–Kawasaki model for slender particles in several space dimensions. Journal of Differential Equations. 284(5), 253–283.","ieee":"F. Cornalba, T. Shardlow, and J. Zimmer, “Well-posedness for a regularised inertial Dean–Kawasaki model for slender particles in several space dimensions,” Journal of Differential Equations, vol. 284, no. 5. Elsevier, pp. 253–283, 2021.","mla":"Cornalba, Federico, et al. “Well-Posedness for a Regularised Inertial Dean–Kawasaki Model for Slender Particles in Several Space Dimensions.” Journal of Differential Equations, vol. 284, no. 5, Elsevier, 2021, pp. 253–83, doi:10.1016/j.jde.2021.02.048.","apa":"Cornalba, F., Shardlow, T., & Zimmer, J. (2021). Well-posedness for a regularised inertial Dean–Kawasaki model for slender particles in several space dimensions. Journal of Differential Equations. Elsevier. https://doi.org/10.1016/j.jde.2021.02.048","ama":"Cornalba F, Shardlow T, Zimmer J. Well-posedness for a regularised inertial Dean–Kawasaki model for slender particles in several space dimensions. Journal of Differential Equations. 2021;284(5):253-283. doi:10.1016/j.jde.2021.02.048","chicago":"Cornalba, Federico, Tony Shardlow, and Johannes Zimmer. “Well-Posedness for a Regularised Inertial Dean–Kawasaki Model for Slender Particles in Several Space Dimensions.” Journal of Differential Equations. Elsevier, 2021. https://doi.org/10.1016/j.jde.2021.02.048."},"volume":284,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","doi":"10.1016/j.jde.2021.02.048","scopus_import":"1","isi":1,"file":[{"file_name":"2021_JourDiffEquations_Cornalba.pdf","success":1,"date_created":"2021-03-22T07:18:01Z","access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_size":473310,"file_id":"9267","date_updated":"2021-03-22T07:18:01Z","checksum":"c630b691fb9e716b02aa6103a9794ec8","creator":"dernst"}],"article_processing_charge":"Yes (via OA deal)"},{"date_updated":"2025-03-31T16:00:58Z","department":[{"_id":"JuFi"}],"has_accepted_license":"1","type":"journal_article","page":"892–939","status":"public","publication":"Stochastics and Partial Differential Equations: Analysis and Computations","date_published":"2021-03-21T00:00:00Z","month":"03","ddc":["510"],"file_date_updated":"2021-04-06T09:31:28Z","day":"21","language":[{"iso":"eng"}],"date_created":"2021-04-04T22:01:21Z","author":[{"orcid":"0000-0001-7252-8072","full_name":"Hensel, Sebastian","first_name":"Sebastian","id":"4D23B7DA-F248-11E8-B48F-1D18A9856A87","last_name":"Hensel"}],"article_type":"original","acknowledgement":"This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 665385 . I am very grateful to M. Gerencsér and J. Maas for proposing this problem as well as helpful discussions. Special thanks go to F. Cornalba for suggesting the additional κ-truncation in Proposition 5. I am also indebted to an anonymous referee for pointing out a gap in a previous version of the proof of Lemma 9 (concerning the treatment of the noise term). The issue is resolved in this version.","scopus_import":"1","isi":1,"article_processing_charge":"Yes (via OA deal)","file":[{"relation":"main_file","access_level":"open_access","date_created":"2021-04-06T09:31:28Z","file_name":"2021_StochPartDiffEquation_Hensel.pdf","success":1,"checksum":"6529b609c9209861720ffa4685111bc6","creator":"dernst","date_updated":"2021-04-06T09:31:28Z","file_id":"9309","file_size":727005,"content_type":"application/pdf"}],"volume":9,"citation":{"ieee":"S. Hensel, “Finite time extinction for the 1D stochastic porous medium equation with transport noise,” Stochastics and Partial Differential Equations: Analysis and Computations, vol. 9. Springer Nature, pp. 892–939, 2021.","ista":"Hensel S. 2021. Finite time extinction for the 1D stochastic porous medium equation with transport noise. Stochastics and Partial Differential Equations: Analysis and Computations. 9, 892–939.","short":"S. Hensel, Stochastics and Partial Differential Equations: Analysis and Computations 9 (2021) 892–939.","chicago":"Hensel, Sebastian. “Finite Time Extinction for the 1D Stochastic Porous Medium Equation with Transport Noise.” Stochastics and Partial Differential Equations: Analysis and Computations. Springer Nature, 2021. https://doi.org/10.1007/s40072-021-00188-9.","mla":"Hensel, Sebastian. “Finite Time Extinction for the 1D Stochastic Porous Medium Equation with Transport Noise.” Stochastics and Partial Differential Equations: Analysis and Computations, vol. 9, Springer Nature, 2021, pp. 892–939, doi:10.1007/s40072-021-00188-9.","ama":"Hensel S. Finite time extinction for the 1D stochastic porous medium equation with transport noise. Stochastics and Partial Differential Equations: Analysis and Computations. 2021;9:892–939. doi:10.1007/s40072-021-00188-9","apa":"Hensel, S. (2021). Finite time extinction for the 1D stochastic porous medium equation with transport noise. Stochastics and Partial Differential Equations: Analysis and Computations. Springer Nature. https://doi.org/10.1007/s40072-021-00188-9"},"quality_controlled":"1","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","doi":"10.1007/s40072-021-00188-9","title":"Finite time extinction for the 1D stochastic porous medium equation with transport noise","publication_status":"published","_id":"9307","oa_version":"Published Version","ec_funded":1,"oa":1,"intvolume":" 9","abstract":[{"text":"We establish finite time extinction with probability one for weak solutions of the Cauchy–Dirichlet problem for the 1D stochastic porous medium equation with Stratonovich transport noise and compactly supported smooth initial datum. Heuristically, this is expected to hold because Brownian motion has average spread rate O(t12) whereas the support of solutions to the deterministic PME grows only with rate O(t1m+1). The rigorous proof relies on a contraction principle up to time-dependent shift for Wong–Zakai type approximations, the transformation to a deterministic PME with two copies of a Brownian path as the lateral boundary, and techniques from the theory of viscosity solutions.","lang":"eng"}],"year":"2021","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"project":[{"_id":"2564DBCA-B435-11E9-9278-68D0E5697425","name":"International IST Doctoral Program","grant_number":"665385","call_identifier":"H2020"}],"publication_identifier":{"eissn":["2194-041X"],"issn":["2194-0401"]},"external_id":{"isi":["000631001700001"]},"publisher":"Springer Nature"},{"scopus_import":"1","article_processing_charge":"No","isi":1,"quality_controlled":"1","citation":{"mla":"Fischer, Julian L., and Daniel Matthes. “The Waiting Time Phenomenon in Spatially Discretized Porous Medium and Thin Film Equations.” SIAM Journal on Numerical Analysis, vol. 59, no. 1, Society for Industrial and Applied Mathematics, 2021, pp. 60–87, doi:10.1137/19M1300017.","ama":"Fischer JL, Matthes D. The waiting time phenomenon in spatially discretized porous medium and thin film equations. SIAM Journal on Numerical Analysis. 2021;59(1):60-87. doi:10.1137/19M1300017","apa":"Fischer, J. L., & Matthes, D. (2021). The waiting time phenomenon in spatially discretized porous medium and thin film equations. SIAM Journal on Numerical Analysis. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/19M1300017","chicago":"Fischer, Julian L, and Daniel Matthes. “The Waiting Time Phenomenon in Spatially Discretized Porous Medium and Thin Film Equations.” SIAM Journal on Numerical Analysis. Society for Industrial and Applied Mathematics, 2021. https://doi.org/10.1137/19M1300017.","ista":"Fischer JL, Matthes D. 2021. The waiting time phenomenon in spatially discretized porous medium and thin film equations. SIAM Journal on Numerical Analysis. 59(1), 60–87.","short":"J.L. Fischer, D. Matthes, SIAM Journal on Numerical Analysis 59 (2021) 60–87.","ieee":"J. L. Fischer and D. Matthes, “The waiting time phenomenon in spatially discretized porous medium and thin film equations,” SIAM Journal on Numerical Analysis, vol. 59, no. 1. Society for Industrial and Applied Mathematics, pp. 60–87, 2021."},"volume":59,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","doi":"10.1137/19M1300017","type":"journal_article","issue":"1","department":[{"_id":"JuFi"}],"date_updated":"2023-08-08T13:10:40Z","date_published":"2021-01-01T00:00:00Z","month":"01","publication":"SIAM Journal on Numerical Analysis","status":"public","page":"60-87","author":[{"last_name":"Fischer","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","first_name":"Julian L","full_name":"Fischer, Julian L","orcid":"0000-0002-0479-558X"},{"last_name":"Matthes","first_name":"Daniel","full_name":"Matthes, Daniel"}],"date_created":"2021-04-18T22:01:42Z","language":[{"iso":"eng"}],"day":"01","article_type":"original","acknowledgement":"This research was supported by the DFG Collaborative Research Center TRR 109, “Discretization in Geometry and Dynamics”.","external_id":{"arxiv":["1911.04185"],"isi":["000625044600003"]},"publication_identifier":{"issn":["0036-1429"]},"publisher":"Society for Industrial and Applied Mathematics","oa_version":"Preprint","publication_status":"published","_id":"9335","title":"The waiting time phenomenon in spatially discretized porous medium and thin film equations","intvolume":" 59","oa":1,"arxiv":1,"main_file_link":[{"url":"https://arxiv.org/abs/1911.04185","open_access":"1"}],"year":"2021","abstract":[{"text":"Various degenerate diffusion equations exhibit a waiting time phenomenon: depending on the “flatness” of the compactly supported initial datum at the boundary of the support, the support of the solution may not expand for a certain amount of time. We show that this phenomenon is captured by particular Lagrangian discretizations of the porous medium and the thin film equations, and we obtain sufficient criteria for the occurrence of waiting times that are consistent with the known ones for the original PDEs. For the spatially discrete solution, the waiting time phenomenon refers to a deviation of the edge of support from its original position by a quantity comparable to the mesh width, over a mesh-independent time interval. Our proof is based on estimates on the fluid velocity in Lagrangian coordinates. Combining weighted entropy estimates with an iteration technique à la Stampacchia leads to upper bounds on free boundary propagation. Numerical simulations show that the phenomenon is already clearly visible for relatively coarse discretizations.","lang":"eng"}]},{"citation":{"chicago":"Fischer, Julian L, Dietmar Gallistl, and Dietmar Peterseim. “A Priori Error Analysis of a Numerical Stochastic Homogenization Method.” SIAM Journal on Numerical Analysis. Society for Industrial and Applied Mathematics, 2021. https://doi.org/10.1137/19M1308992.","mla":"Fischer, Julian L., et al. “A Priori Error Analysis of a Numerical Stochastic Homogenization Method.” SIAM Journal on Numerical Analysis, vol. 59, no. 2, Society for Industrial and Applied Mathematics, 2021, pp. 660–74, doi:10.1137/19M1308992.","ama":"Fischer JL, Gallistl D, Peterseim D. A priori error analysis of a numerical stochastic homogenization method. SIAM Journal on Numerical Analysis. 2021;59(2):660-674. doi:10.1137/19M1308992","apa":"Fischer, J. L., Gallistl, D., & Peterseim, D. (2021). A priori error analysis of a numerical stochastic homogenization method. SIAM Journal on Numerical Analysis. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/19M1308992","ieee":"J. L. Fischer, D. Gallistl, and D. Peterseim, “A priori error analysis of a numerical stochastic homogenization method,” SIAM Journal on Numerical Analysis, vol. 59, no. 2. Society for Industrial and Applied Mathematics, pp. 660–674, 2021.","ista":"Fischer JL, Gallistl D, Peterseim D. 2021. A priori error analysis of a numerical stochastic homogenization method. SIAM Journal on Numerical Analysis. 59(2), 660–674.","short":"J.L. Fischer, D. Gallistl, D. Peterseim, SIAM Journal on Numerical Analysis 59 (2021) 660–674."},"quality_controlled":"1","volume":59,"doi":"10.1137/19M1308992","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","scopus_import":"1","isi":1,"article_processing_charge":"No","language":[{"iso":"eng"}],"day":"09","date_created":"2021-04-25T22:01:31Z","author":[{"orcid":"0000-0002-0479-558X","full_name":"Fischer, Julian L","first_name":"Julian L","last_name":"Fischer","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Gallistl, Dietmar","last_name":"Gallistl","first_name":"Dietmar"},{"first_name":"Dietmar","last_name":"Peterseim","full_name":"Peterseim, Dietmar"}],"article_type":"original","acknowledgement":"This work was initiated while the authors enjoyed the kind hospitality of the Hausdorff Institute for Mathematics in Bonn during the trimester program Multiscale Problems: Algorithms, Numerical Analysis, and Computation. D. Peterseim would like to acknowledge the kind hospitality of the Erwin Schrödinger International Institute for Mathematics and Physics (ESI), where parts of this research were developed under the frame of the thematic program Numerical Analysis of Complex PDE Models in the Sciences.","date_updated":"2023-08-08T13:13:37Z","type":"journal_article","issue":"2","department":[{"_id":"JuFi"}],"status":"public","page":"660-674","date_published":"2021-03-09T00:00:00Z","month":"03","publication":"SIAM Journal on Numerical Analysis","publisher":"Society for Industrial and Applied Mathematics","publication_identifier":{"issn":["0036-1429"]},"external_id":{"isi":["000646030400003"],"arxiv":["1912.11646"]},"arxiv":1,"year":"2021","abstract":[{"text":"This paper provides an a priori error analysis of a localized orthogonal decomposition method for the numerical stochastic homogenization of a model random diffusion problem. If the uniformly elliptic and bounded random coefficient field of the model problem is stationary and satisfies a quantitative decorrelation assumption in the form of the spectral gap inequality, then the expected $L^2$ error of the method can be estimated, up to logarithmic factors, by $H+(\\varepsilon/H)^{d/2}$, $\\varepsilon$ being the small correlation length of the random coefficient and $H$ the width of the coarse finite element mesh that determines the spatial resolution. The proof bridges recent results of numerical homogenization and quantitative stochastic homogenization.","lang":"eng"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1912.11646"}],"publication_status":"published","_id":"9352","title":"A priori error analysis of a numerical stochastic homogenization method","oa_version":"Preprint","intvolume":" 59","oa":1},{"oa":1,"intvolume":" 31","oa_version":"Published Version","title":"On the dynamic slip boundary condition for Navier-Stokes-like problems","_id":"10575","publication_status":"published","abstract":[{"text":"The choice of the boundary conditions in mechanical problems has to reflect the interaction of the considered material with the surface. Still the assumption of the no-slip condition is preferred in order to avoid boundary terms in the analysis and slipping effects are usually overlooked. Besides the “static slip models”, there are phenomena that are not accurately described by them, e.g. at the moment when the slip changes rapidly, the wall shear stress and the slip can exhibit a sudden overshoot and subsequent relaxation. When these effects become significant, the so-called dynamic slip phenomenon occurs. We develop a mathematical analysis of Navier–Stokes-like problems with a dynamic slip boundary condition, which requires a proper generalization of the Gelfand triplet and the corresponding function space setting.","lang":"eng"}],"year":"2021","arxiv":1,"external_id":{"isi":["000722309400001"],"arxiv":["2009.09057"]},"license":"https://creativecommons.org/licenses/by-nc-nd/4.0/","publication_identifier":{"issn":["0218-2025"],"eissn":["1793-6314"]},"project":[{"name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504"},{"call_identifier":"FWF","grant_number":"W1245","_id":"260788DE-B435-11E9-9278-68D0E5697425","name":"Dissipation and dispersion in nonlinear partial differential equations"}],"tmp":{"short":"CC BY-NC-ND (4.0)","image":"/images/cc_by_nc_nd.png","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode"},"publisher":"World Scientific Publishing","publication":"Mathematical Models and Methods in Applied Sciences","month":"10","ddc":["510"],"date_published":"2021-10-13T00:00:00Z","page":"2165-2212","status":"public","has_accepted_license":"1","department":[{"_id":"JuFi"}],"issue":"11","type":"journal_article","date_updated":"2025-04-15T08:31:30Z","article_type":"original","acknowledgement":"The research of A. Abbatiello is supported by Einstein Foundation, Berlin. A. Abbatiello is also member of the Italian National Group for the Mathematical Physics (GNFM) of INdAM. M. Bulíček acknowledges the support of the project No. 20-11027X financed by Czech Science Foundation (GACR). M. Bulíček is member of the Jindřich Nečas Center for Mathematical Modelling. E. Maringová acknowledges support from Charles University Research program UNCE/SCI/023, the grant SVV-2020-260583 by the Ministry of Education, Youth and Sports, Czech Republic and from the Austrian Science Fund (FWF), grants P30000, W1245, and F65.","author":[{"full_name":"Abbatiello, Anna","last_name":"Abbatiello","first_name":"Anna"},{"last_name":"Bulíček","first_name":"Miroslav","full_name":"Bulíček, Miroslav"},{"first_name":"Erika","id":"dbabca31-66eb-11eb-963a-fb9c22c880b4","last_name":"Maringová","full_name":"Maringová, Erika"}],"file_date_updated":"2022-05-16T10:55:45Z","day":"13","date_created":"2021-12-26T23:01:27Z","language":[{"iso":"eng"}],"article_processing_charge":"No","file":[{"file_id":"11385","file_size":795483,"content_type":"application/pdf","checksum":"8c0a9396335f0b70e1f5cbfe450a987a","creator":"dernst","date_updated":"2022-05-16T10:55:45Z","success":1,"file_name":"2021_MathModelsMethods_Abbatiello.pdf","relation":"main_file","date_created":"2022-05-16T10:55:45Z","access_level":"open_access"}],"isi":1,"scopus_import":"1","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","doi":"10.1142/S0218202521500470","volume":31,"quality_controlled":"1","citation":{"chicago":"Abbatiello, Anna, Miroslav Bulíček, and Erika Maringová. “On the Dynamic Slip Boundary Condition for Navier-Stokes-like Problems.” Mathematical Models and Methods in Applied Sciences. World Scientific Publishing, 2021. https://doi.org/10.1142/S0218202521500470.","ama":"Abbatiello A, Bulíček M, Maringová E. On the dynamic slip boundary condition for Navier-Stokes-like problems. Mathematical Models and Methods in Applied Sciences. 2021;31(11):2165-2212. doi:10.1142/S0218202521500470","apa":"Abbatiello, A., Bulíček, M., & Maringová, E. (2021). On the dynamic slip boundary condition for Navier-Stokes-like problems. Mathematical Models and Methods in Applied Sciences. World Scientific Publishing. https://doi.org/10.1142/S0218202521500470","mla":"Abbatiello, Anna, et al. “On the Dynamic Slip Boundary Condition for Navier-Stokes-like Problems.” Mathematical Models and Methods in Applied Sciences, vol. 31, no. 11, World Scientific Publishing, 2021, pp. 2165–212, doi:10.1142/S0218202521500470.","ieee":"A. Abbatiello, M. Bulíček, and E. Maringová, “On the dynamic slip boundary condition for Navier-Stokes-like problems,” Mathematical Models and Methods in Applied Sciences, vol. 31, no. 11. World Scientific Publishing, pp. 2165–2212, 2021.","short":"A. Abbatiello, M. Bulíček, E. Maringová, Mathematical Models and Methods in Applied Sciences 31 (2021) 2165–2212.","ista":"Abbatiello A, Bulíček M, Maringová E. 2021. On the dynamic slip boundary condition for Navier-Stokes-like problems. Mathematical Models and Methods in Applied Sciences. 31(11), 2165–2212."}},{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","doi":"10.1142/S0218202521500457","volume":31,"citation":{"chicago":"Bulíček, Miroslav, Erika Maringová, and Josef Málek. “On Nonlinear Problems of Parabolic Type with Implicit Constitutive Equations Involving Flux.” Mathematical Models and Methods in Applied Sciences. World Scientific Publishing, 2021. https://doi.org/10.1142/S0218202521500457.","ama":"Bulíček M, Maringová E, Málek J. On nonlinear problems of parabolic type with implicit constitutive equations involving flux. Mathematical Models and Methods in Applied Sciences. 2021;31(09). doi:10.1142/S0218202521500457","apa":"Bulíček, M., Maringová, E., & Málek, J. (2021). On nonlinear problems of parabolic type with implicit constitutive equations involving flux. Mathematical Models and Methods in Applied Sciences. World Scientific Publishing. https://doi.org/10.1142/S0218202521500457","mla":"Bulíček, Miroslav, et al. “On Nonlinear Problems of Parabolic Type with Implicit Constitutive Equations Involving Flux.” Mathematical Models and Methods in Applied Sciences, vol. 31, no. 09, World Scientific Publishing, 2021, doi:10.1142/S0218202521500457.","ieee":"M. Bulíček, E. Maringová, and J. Málek, “On nonlinear problems of parabolic type with implicit constitutive equations involving flux,” Mathematical Models and Methods in Applied Sciences, vol. 31, no. 09. World Scientific Publishing, 2021.","short":"M. Bulíček, E. Maringová, J. Málek, Mathematical Models and Methods in Applied Sciences 31 (2021).","ista":"Bulíček M, Maringová E, Málek J. 2021. On nonlinear problems of parabolic type with implicit constitutive equations involving flux. Mathematical Models and Methods in Applied Sciences. 31(09)."},"quality_controlled":"1","isi":1,"article_processing_charge":"No","scopus_import":"1","article_type":"original","acknowledgement":"M. Bulíček and J. Málek acknowledge the support of the project No. 18-12719S financed by the Czech\r\nScience foundation (GAČR). E. Maringová acknowledges support from Charles University Research program \r\nUNCE/SCI/023, the grant SVV-2020-260583 by the Ministry of Education, Youth and Sports, Czech Republic\r\nand from the Austrian Science Fund (FWF), grants P30000, W1245, and F65. M. Bulíček and J. Málek are\r\nmembers of the Nečas Center for Mathematical Modelling.\r\n","day":"25","language":[{"iso":"eng"}],"date_created":"2021-09-12T22:01:25Z","author":[{"full_name":"Bulíček, Miroslav","last_name":"Bulíček","first_name":"Miroslav"},{"full_name":"Maringová, Erika","first_name":"Erika","last_name":"Maringová","id":"dbabca31-66eb-11eb-963a-fb9c22c880b4"},{"full_name":"Málek, Josef","last_name":"Málek","first_name":"Josef"}],"status":"public","publication":"Mathematical Models and Methods in Applied Sciences","date_published":"2021-08-25T00:00:00Z","month":"08","date_updated":"2026-08-18T07:47:39Z","department":[{"_id":"JuFi"}],"issue":"09","type":"journal_article","publisher":"World Scientific Publishing","publication_identifier":{"eissn":["1793-6314"],"issn":["0218-2025"]},"external_id":{"isi":["000722222900004"],"arxiv":["2009.06917"]},"project":[{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504"}],"keyword":["Nonlinear parabolic systems","implicit constitutive theory","weak solutions","existence","uniqueness"],"abstract":[{"text":"We study systems of nonlinear partial differential equations of parabolic type, in which the elliptic operator is replaced by the first-order divergence operator acting on a flux function, which is related to the spatial gradient of the unknown through an additional implicit equation. This setting, broad enough in terms of applications, significantly expands the paradigm of nonlinear parabolic problems. Formulating four conditions concerning the form of the implicit equation, we first show that these conditions describe a maximal monotone p-coercive graph. We then establish the global-in-time and large-data existence of a (weak) solution and its uniqueness. To this end, we adopt and significantly generalize Minty’s method of monotone mappings. A unified theory, containing several novel tools, is developed in a way to be tractable from the point of view of numerical approximations.","lang":"eng"}],"year":"2021","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2009.06917"}],"arxiv":1,"oa":1,"intvolume":" 31","title":"On nonlinear problems of parabolic type with implicit constitutive equations involving flux","_id":"10005","publication_status":"published","oa_version":"Preprint"},{"status":"public","publication":"arXiv","ec_funded":1,"oa":1,"month":"03","date_published":"2020-03-11T00:00:00Z","title":"The local structure of the energy landscape in multiphase mean curvature flow: weak-strong uniqueness and stability of evolutions","date_updated":"2026-04-08T07:01:01Z","_id":"10012","publication_status":"draft","department":[{"_id":"JuFi"}],"oa_version":"Preprint","type":"preprint","abstract":[{"lang":"eng","text":"We prove that in the absence of topological changes, the notion of BV solutions to planar multiphase mean curvature flow does not allow for a mechanism for (unphysical) non-uniqueness. Our approach is based on the local structure of the energy landscape near a classical evolution by mean curvature. Mean curvature flow being the gradient flow of the surface energy functional, we develop a gradient-flow analogue of the notion of calibrations. Just like the existence of a calibration guarantees that one has reached a global minimum in the energy landscape, the existence of a \"gradient flow calibration\" ensures that the route of steepest descent in the energy landscape is unique and stable."}],"acknowledgement":"Parts of the paper were written during the visit of the authors to the Hausdorff Research Institute for Mathematics (HIM), University of Bonn, in the framework of the trimester program “Evolution of Interfaces”. The support and the hospitality of HIM are gratefully acknowledged. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No. 665385.","year":"2020","related_material":{"record":[{"relation":"dissertation_contains","id":"10007","status":"public"}]},"main_file_link":[{"url":"https://arxiv.org/abs/2003.05478","open_access":"1"}],"date_created":"2021-09-13T12:17:11Z","language":[{"iso":"eng"}],"day":"11","arxiv":1,"author":[{"first_name":"Julian L","last_name":"Fischer","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0479-558X","full_name":"Fischer, Julian L"},{"first_name":"Sebastian","last_name":"Hensel","id":"4D23B7DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-7252-8072","full_name":"Hensel, Sebastian"},{"full_name":"Laux, Tim","last_name":"Laux","first_name":"Tim"},{"full_name":"Simon, Thilo","first_name":"Thilo","last_name":"Simon"}],"article_processing_charge":"No","external_id":{"arxiv":["2003.05478"]},"project":[{"_id":"2564DBCA-B435-11E9-9278-68D0E5697425","name":"International IST Doctoral Program","call_identifier":"H2020","grant_number":"665385"}],"doi":"10.48550/arXiv.2003.05478","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_number":"2003.05478","citation":{"ista":"Fischer JL, Hensel S, Laux T, Simon T. The local structure of the energy landscape in multiphase mean curvature flow: weak-strong uniqueness and stability of evolutions. arXiv, 2003.05478.","short":"J.L. Fischer, S. Hensel, T. Laux, T. Simon, ArXiv (n.d.).","ieee":"J. L. Fischer, S. Hensel, T. Laux, and T. Simon, “The local structure of the energy landscape in multiphase mean curvature flow: weak-strong uniqueness and stability of evolutions,” arXiv. .","mla":"Fischer, Julian L., et al. “The Local Structure of the Energy Landscape in Multiphase Mean Curvature Flow: Weak-Strong Uniqueness and Stability of Evolutions.” ArXiv, 2003.05478, doi:10.48550/arXiv.2003.05478.","ama":"Fischer JL, Hensel S, Laux T, Simon T. The local structure of the energy landscape in multiphase mean curvature flow: weak-strong uniqueness and stability of evolutions. arXiv. doi:10.48550/arXiv.2003.05478","apa":"Fischer, J. L., Hensel, S., Laux, T., & Simon, T. (n.d.). The local structure of the energy landscape in multiphase mean curvature flow: weak-strong uniqueness and stability of evolutions. arXiv. https://doi.org/10.48550/arXiv.2003.05478","chicago":"Fischer, Julian L, Sebastian Hensel, Tim Laux, and Thilo Simon. “The Local Structure of the Energy Landscape in Multiphase Mean Curvature Flow: Weak-Strong Uniqueness and Stability of Evolutions.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2003.05478."}},{"department":[{"_id":"JuFi"}],"type":"journal_article","issue":"2","date_updated":"2026-04-02T14:26:08Z","publication":"Nonlinearity","month":"01","date_published":"2020-01-10T00:00:00Z","page":"864-891","status":"public","author":[{"id":"2CEB641C-A400-11E9-A717-D712E6697425","last_name":"Cornalba","first_name":"Federico","full_name":"Cornalba, Federico","orcid":"0000-0002-6269-5149"},{"first_name":"Tony","last_name":"Shardlow","full_name":"Shardlow, Tony"},{"full_name":"Zimmer, Johannes","last_name":"Zimmer","first_name":"Johannes"}],"day":"10","language":[{"iso":"eng"}],"date_created":"2020-04-05T22:00:49Z","article_type":"original","scopus_import":"1","article_processing_charge":"No","isi":1,"volume":33,"citation":{"ieee":"F. Cornalba, T. Shardlow, and J. Zimmer, “From weakly interacting particles to a regularised Dean-Kawasaki model,” Nonlinearity, vol. 33, no. 2. IOP Publishing, pp. 864–891, 2020.","short":"F. Cornalba, T. Shardlow, J. Zimmer, Nonlinearity 33 (2020) 864–891.","ista":"Cornalba F, Shardlow T, Zimmer J. 2020. From weakly interacting particles to a regularised Dean-Kawasaki model. Nonlinearity. 33(2), 864–891.","chicago":"Cornalba, Federico, Tony Shardlow, and Johannes Zimmer. “From Weakly Interacting Particles to a Regularised Dean-Kawasaki Model.” Nonlinearity. IOP Publishing, 2020. https://doi.org/10.1088/1361-6544/ab5174.","apa":"Cornalba, F., Shardlow, T., & Zimmer, J. (2020). From weakly interacting particles to a regularised Dean-Kawasaki model. Nonlinearity. IOP Publishing. https://doi.org/10.1088/1361-6544/ab5174","ama":"Cornalba F, Shardlow T, Zimmer J. From weakly interacting particles to a regularised Dean-Kawasaki model. Nonlinearity. 2020;33(2):864-891. doi:10.1088/1361-6544/ab5174","mla":"Cornalba, Federico, et al. “From Weakly Interacting Particles to a Regularised Dean-Kawasaki Model.” Nonlinearity, vol. 33, no. 2, IOP Publishing, 2020, pp. 864–91, doi:10.1088/1361-6544/ab5174."},"quality_controlled":"1","doi":"10.1088/1361-6544/ab5174","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","oa_version":"Preprint","title":"From weakly interacting particles to a regularised Dean-Kawasaki model","_id":"7637","publication_status":"published","oa":1,"intvolume":" 33","arxiv":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1811.06448"}],"abstract":[{"lang":"eng","text":"The evolution of finitely many particles obeying Langevin dynamics is described by Dean–Kawasaki equations, a class of stochastic equations featuring a non-Lipschitz multiplicative noise in divergence form. We derive a regularised Dean–Kawasaki model based on second order Langevin dynamics by analysing a system of particles interacting via a pairwise potential. Key tools of our analysis are the propagation of chaos and Simon's compactness criterion. The model we obtain is a small-noise stochastic perturbation of the undamped McKean–Vlasov equation. We also provide a high-probability result for existence and uniqueness for our model."}],"year":"2020","external_id":{"arxiv":["1811.06448"],"isi":["000508175400001"]},"publication_identifier":{"eissn":["1361-6544"],"issn":["0951-7715"]},"publisher":"IOP Publishing"},{"publisher":"Springer Nature","publication_identifier":{"eissn":["2296-9039"],"issn":["2296-9020"]},"external_id":{"pmid":["33195442"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"project":[{"_id":"3AC91DDA-15DF-11EA-824D-93A3E7B544D1","name":"FWF Open Access Fund","call_identifier":"FWF"}],"abstract":[{"text":"In this paper, we establish convergence to equilibrium for a drift–diffusion–recombination system modelling the charge transport within certain semiconductor devices. More precisely, we consider a two-level system for electrons and holes which is augmented by an intermediate energy level for electrons in so-called trapped states. The recombination dynamics use the mass action principle by taking into account this additional trap level. The main part of the paper is concerned with the derivation of an entropy–entropy production inequality, which entails exponential convergence to the equilibrium via the so-called entropy method. The novelty of our approach lies in the fact that the entropy method is applied uniformly in a fast-reaction parameter which governs the lifetime of electrons on the trap level. Thus, the resulting decay estimate for the densities of electrons and holes extends to the corresponding quasi-steady-state approximation.","lang":"eng"}],"year":"2020","pmid":1,"oa":1,"intvolume":" 6","title":"Uniform convergence to equilibrium for a family of drift–diffusion models with trap-assisted recombination and the limiting Shockley–Read–Hall model","_id":"7866","publication_status":"published","oa_version":"Published Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","doi":"10.1007/s41808-020-00068-8","volume":6,"quality_controlled":"1","citation":{"apa":"Fellner, K., & Kniely, M. (2020). Uniform convergence to equilibrium for a family of drift–diffusion models with trap-assisted recombination and the limiting Shockley–Read–Hall model. Journal of Elliptic and Parabolic Equations. Springer Nature. https://doi.org/10.1007/s41808-020-00068-8","ama":"Fellner K, Kniely M. Uniform convergence to equilibrium for a family of drift–diffusion models with trap-assisted recombination and the limiting Shockley–Read–Hall model. Journal of Elliptic and Parabolic Equations. 2020;6:529-598. doi:10.1007/s41808-020-00068-8","mla":"Fellner, Klemens, and Michael Kniely. “Uniform Convergence to Equilibrium for a Family of Drift–Diffusion Models with Trap-Assisted Recombination and the Limiting Shockley–Read–Hall Model.” Journal of Elliptic and Parabolic Equations, vol. 6, Springer Nature, 2020, pp. 529–98, doi:10.1007/s41808-020-00068-8.","chicago":"Fellner, Klemens, and Michael Kniely. “Uniform Convergence to Equilibrium for a Family of Drift–Diffusion Models with Trap-Assisted Recombination and the Limiting Shockley–Read–Hall Model.” Journal of Elliptic and Parabolic Equations. Springer Nature, 2020. https://doi.org/10.1007/s41808-020-00068-8.","short":"K. Fellner, M. Kniely, Journal of Elliptic and Parabolic Equations 6 (2020) 529–598.","ista":"Fellner K, Kniely M. 2020. Uniform convergence to equilibrium for a family of drift–diffusion models with trap-assisted recombination and the limiting Shockley–Read–Hall model. Journal of Elliptic and Parabolic Equations. 6, 529–598.","ieee":"K. Fellner and M. Kniely, “Uniform convergence to equilibrium for a family of drift–diffusion models with trap-assisted recombination and the limiting Shockley–Read–Hall model,” Journal of Elliptic and Parabolic Equations, vol. 6. Springer Nature, pp. 529–598, 2020."},"article_processing_charge":"No","file":[{"file_id":"8802","file_size":8408694,"content_type":"application/pdf","creator":"dernst","checksum":"6bc6832caacddceee1471291e93dcf1d","date_updated":"2020-11-25T08:59:59Z","success":1,"file_name":"2020_JourEllipticParabEquat_Fellner.pdf","access_level":"open_access","date_created":"2020-11-25T08:59:59Z","relation":"main_file"}],"scopus_import":"1","acknowledgement":"Open access funding provided by Austrian Science Fund (FWF). The second author has been supported by the International Research Training Group IGDK 1754 “Optimization and Numerical Analysis for Partial Differential Equations with Nonsmooth Structures”, funded by the German Research Council (DFG) and the Austrian Science Fund (FWF) under grant number [W 1244-N18].","corr_author":"1","article_type":"original","file_date_updated":"2020-11-25T08:59:59Z","date_created":"2020-05-17T22:00:45Z","day":"01","language":[{"iso":"eng"}],"author":[{"last_name":"Fellner","first_name":"Klemens","full_name":"Fellner, Klemens"},{"full_name":"Kniely, Michael","orcid":"0000-0001-5645-4333","id":"2CA2C08C-F248-11E8-B48F-1D18A9856A87","last_name":"Kniely","first_name":"Michael"}],"page":"529-598","status":"public","publication":"Journal of Elliptic and Parabolic Equations","ddc":["510"],"date_published":"2020-12-01T00:00:00Z","month":"12","date_updated":"2025-07-17T08:12:24Z","department":[{"_id":"JuFi"}],"has_accepted_license":"1","type":"journal_article"},{"scopus_import":"1","isi":1,"file":[{"date_updated":"2020-10-27T12:09:57Z","checksum":"ed90bc6eb5f32ee6157fef7f3aabc057","creator":"cziletti","content_type":"application/pdf","file_size":1223899,"file_id":"8710","relation":"main_file","date_created":"2020-10-27T12:09:57Z","access_level":"open_access","file_name":"2020_Nonlinearity_Fischer.pdf","success":1}],"article_processing_charge":"Yes (via OA deal)","citation":{"ieee":"J. L. Fischer and M. Kniely, “Variance reduction for effective energies of random lattices in the Thomas-Fermi-von Weizsäcker model,” Nonlinearity, vol. 33, no. 11. IOP Publishing, pp. 5733–5772, 2020.","short":"J.L. Fischer, M. Kniely, Nonlinearity 33 (2020) 5733–5772.","ista":"Fischer JL, Kniely M. 2020. Variance reduction for effective energies of random lattices in the Thomas-Fermi-von Weizsäcker model. Nonlinearity. 33(11), 5733–5772.","chicago":"Fischer, Julian L, and Michael Kniely. “Variance Reduction for Effective Energies of Random Lattices in the Thomas-Fermi-von Weizsäcker Model.” Nonlinearity. IOP Publishing, 2020. https://doi.org/10.1088/1361-6544/ab9728.","apa":"Fischer, J. L., & Kniely, M. (2020). Variance reduction for effective energies of random lattices in the Thomas-Fermi-von Weizsäcker model. Nonlinearity. IOP Publishing. https://doi.org/10.1088/1361-6544/ab9728","ama":"Fischer JL, Kniely M. Variance reduction for effective energies of random lattices in the Thomas-Fermi-von Weizsäcker model. Nonlinearity. 2020;33(11):5733-5772. doi:10.1088/1361-6544/ab9728","mla":"Fischer, Julian L., and Michael Kniely. “Variance Reduction for Effective Energies of Random Lattices in the Thomas-Fermi-von Weizsäcker Model.” Nonlinearity, vol. 33, no. 11, IOP Publishing, 2020, pp. 5733–72, doi:10.1088/1361-6544/ab9728."},"quality_controlled":"1","volume":33,"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","doi":"10.1088/1361-6544/ab9728","date_updated":"2026-04-02T14:31:34Z","issue":"11","type":"journal_article","has_accepted_license":"1","department":[{"_id":"JuFi"}],"status":"public","page":"5733-5772","month":"11","ddc":["510"],"date_published":"2020-11-01T00:00:00Z","publication":"Nonlinearity","language":[{"iso":"eng"}],"date_created":"2020-10-25T23:01:16Z","day":"01","file_date_updated":"2020-10-27T12:09:57Z","author":[{"last_name":"Fischer","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","first_name":"Julian L","full_name":"Fischer, Julian L","orcid":"0000-0002-0479-558X"},{"orcid":"0000-0001-5645-4333","full_name":"Kniely, Michael","first_name":"Michael","last_name":"Kniely","id":"2CA2C08C-F248-11E8-B48F-1D18A9856A87"}],"corr_author":"1","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/3.0/legalcode","name":"Creative Commons Attribution 3.0 Unported (CC BY 3.0)","short":"CC BY (3.0)","image":"/images/cc_by.png"},"publication_identifier":{"eissn":["1361-6544"],"issn":["0951-7715"]},"license":"https://creativecommons.org/licenses/by/3.0/","external_id":{"arxiv":["1906.12245"],"isi":["000576492700001"]},"publisher":"IOP Publishing","_id":"8697","publication_status":"published","title":"Variance reduction for effective energies of random lattices in the Thomas-Fermi-von Weizsäcker model","oa_version":"Published Version","intvolume":" 33","oa":1,"arxiv":1,"year":"2020","abstract":[{"lang":"eng","text":"In the computation of the material properties of random alloys, the method of 'special quasirandom structures' attempts to approximate the properties of the alloy on a finite volume with higher accuracy by replicating certain statistics of the random atomic lattice in the finite volume as accurately as possible. In the present work, we provide a rigorous justification for a variant of this method in the framework of the Thomas–Fermi–von Weizsäcker (TFW) model. Our approach is based on a recent analysis of a related variance reduction method in stochastic homogenization of linear elliptic PDEs and the locality properties of the TFW model. Concerning the latter, we extend an exponential locality result by Nazar and Ortner to include point charges, a result that may be of independent interest."}]},{"isi":1,"article_processing_charge":"No","file":[{"file_name":"2020_SIAM_Fischer.pdf","success":1,"relation":"main_file","access_level":"open_access","date_created":"2021-01-25T07:48:39Z","file_id":"9041","content_type":"application/pdf","file_size":310655,"creator":"dernst","checksum":"21aa1cf4c30a86a00cae15a984819b5d","date_updated":"2021-01-25T07:48:39Z"}],"scopus_import":"1","doi":"10.1137/20M1322182","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","volume":52,"quality_controlled":"1","citation":{"ista":"Fischer JL, Laux T, Simon TM. 2020. Convergence rates of the Allen-Cahn equation to mean curvature flow: A short proof based on relative entropies. SIAM Journal on Mathematical Analysis. 52(6), 6222–6233.","short":"J.L. Fischer, T. Laux, T.M. Simon, SIAM Journal on Mathematical Analysis 52 (2020) 6222–6233.","ieee":"J. L. Fischer, T. Laux, and T. M. Simon, “Convergence rates of the Allen-Cahn equation to mean curvature flow: A short proof based on relative entropies,” SIAM Journal on Mathematical Analysis, vol. 52, no. 6. Society for Industrial and Applied Mathematics, pp. 6222–6233, 2020.","ama":"Fischer JL, Laux T, Simon TM. Convergence rates of the Allen-Cahn equation to mean curvature flow: A short proof based on relative entropies. SIAM Journal on Mathematical Analysis. 2020;52(6):6222-6233. doi:10.1137/20M1322182","apa":"Fischer, J. L., Laux, T., & Simon, T. M. (2020). Convergence rates of the Allen-Cahn equation to mean curvature flow: A short proof based on relative entropies. SIAM Journal on Mathematical Analysis. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/20M1322182","mla":"Fischer, Julian L., et al. “Convergence Rates of the Allen-Cahn Equation to Mean Curvature Flow: A Short Proof Based on Relative Entropies.” SIAM Journal on Mathematical Analysis, vol. 52, no. 6, Society for Industrial and Applied Mathematics, 2020, pp. 6222–33, doi:10.1137/20M1322182.","chicago":"Fischer, Julian L, Tim Laux, and Theresa M. Simon. “Convergence Rates of the Allen-Cahn Equation to Mean Curvature Flow: A Short Proof Based on Relative Entropies.” SIAM Journal on Mathematical Analysis. Society for Industrial and Applied Mathematics, 2020. https://doi.org/10.1137/20M1322182."},"page":"6222-6233","status":"public","publication":"SIAM Journal on Mathematical Analysis","month":"12","date_published":"2020-12-15T00:00:00Z","ddc":["510"],"date_updated":"2025-07-10T12:01:32Z","department":[{"_id":"JuFi"}],"has_accepted_license":"1","type":"journal_article","issue":"6","article_type":"original","acknowledgement":"This work was supported by the European Union's Horizon 2020 Research and Innovation\r\nProgramme under Marie Sklodowska-Curie grant agreement 665385 and by the Deutsche\r\nForschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy, EXC-2047/1--390685813.","corr_author":"1","file_date_updated":"2021-01-25T07:48:39Z","language":[{"iso":"eng"}],"date_created":"2021-01-24T23:01:09Z","day":"15","author":[{"full_name":"Fischer, Julian L","orcid":"0000-0002-0479-558X","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","last_name":"Fischer","first_name":"Julian L"},{"full_name":"Laux, Tim","first_name":"Tim","last_name":"Laux"},{"full_name":"Simon, Theresa M.","last_name":"Simon","first_name":"Theresa M."}],"publication_identifier":{"eissn":["1095-7154"],"issn":["0036-1410"]},"external_id":{"isi":["000600695200027"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"project":[{"name":"International IST Doctoral Program","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"665385"}],"publisher":"Society for Industrial and Applied Mathematics","oa":1,"ec_funded":1,"intvolume":" 52","title":"Convergence rates of the Allen-Cahn equation to mean curvature flow: A short proof based on relative entropies","publication_status":"published","_id":"9039","oa_version":"Published Version","abstract":[{"lang":"eng","text":"We give a short and self-contained proof for rates of convergence of the Allen--Cahn equation towards mean curvature flow, assuming that a classical (smooth) solution to the latter exists and starting from well-prepared initial data. Our approach is based on a relative entropy technique. In particular, it does not require a stability analysis for the linearized Allen--Cahn operator. As our analysis also does not rely on the comparison principle, we expect it to be applicable to more complex equations and systems."}],"year":"2020"},{"external_id":{"arxiv":["1709.05202"],"isi":["000558100500002"]},"publication_identifier":{"eissn":["1730-6337"],"issn":["0039-3223"]},"publisher":"Instytut Matematyczny","intvolume":" 252","oa":1,"oa_version":"Preprint","publication_status":"published","_id":"9196","title":"Modelled distributions of Triebel–Lizorkin type","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1709.05202","open_access":"1"}],"year":"2020","abstract":[{"lang":"eng","text":"In order to provide a local description of a regular function in a small neighbourhood of a point x, it is sufficient by Taylor’s theorem to know the value of the function as well as all of its derivatives up to the required order at the point x itself. In other words, one could say that a regular function is locally modelled by the set of polynomials. The theory of regularity structures due to Hairer generalizes this observation and provides an abstract setup, which in the application to singular SPDE extends the set of polynomials by functionals constructed from, e.g., white noise. In this context, the notion of Taylor polynomials is lifted to the notion of so-called modelled distributions. The celebrated reconstruction theorem, which in turn was inspired by Gubinelli’s \\textit {sewing lemma}, is of paramount importance for the theory. It enables one to reconstruct a modelled distribution as a true distribution on Rd which is locally approximated by this extended set of models or “monomials”. In the original work of Hairer, the error is measured by means of Hölder norms. This was then generalized to the whole scale of Besov spaces by Hairer and Labbé. It is the aim of this work to adapt the analytic part of the theory of regularity structures to the scale of Triebel–Lizorkin spaces."}],"keyword":["General Mathematics"],"arxiv":1,"article_processing_charge":"No","isi":1,"scopus_import":"1","doi":"10.4064/sm180411-11-2","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Hensel S, Rosati T. 2020. Modelled distributions of Triebel–Lizorkin type. Studia Mathematica. 252(3), 251–297.","short":"S. Hensel, T. Rosati, Studia Mathematica 252 (2020) 251–297.","ieee":"S. Hensel and T. Rosati, “Modelled distributions of Triebel–Lizorkin type,” Studia Mathematica, vol. 252, no. 3. Instytut Matematyczny, pp. 251–297, 2020.","mla":"Hensel, Sebastian, and Tommaso Rosati. “Modelled Distributions of Triebel–Lizorkin Type.” Studia Mathematica, vol. 252, no. 3, Instytut Matematyczny, 2020, pp. 251–97, doi:10.4064/sm180411-11-2.","apa":"Hensel, S., & Rosati, T. (2020). Modelled distributions of Triebel–Lizorkin type. Studia Mathematica. Instytut Matematyczny. https://doi.org/10.4064/sm180411-11-2","ama":"Hensel S, Rosati T. Modelled distributions of Triebel–Lizorkin type. Studia Mathematica. 2020;252(3):251-297. doi:10.4064/sm180411-11-2","chicago":"Hensel, Sebastian, and Tommaso Rosati. “Modelled Distributions of Triebel–Lizorkin Type.” Studia Mathematica. Instytut Matematyczny, 2020. https://doi.org/10.4064/sm180411-11-2."},"quality_controlled":"1","volume":252,"date_published":"2020-03-01T00:00:00Z","month":"03","publication":"Studia Mathematica","status":"public","page":"251-297","issue":"3","type":"journal_article","department":[{"_id":"JuFi"},{"_id":"GradSch"}],"date_updated":"2025-06-24T12:07:06Z","article_type":"original","author":[{"last_name":"Hensel","id":"4D23B7DA-F248-11E8-B48F-1D18A9856A87","first_name":"Sebastian","full_name":"Hensel, Sebastian","orcid":"0000-0001-7252-8072"},{"last_name":"Rosati","first_name":"Tommaso","full_name":"Rosati, Tommaso"}],"language":[{"iso":"eng"}],"day":"01","date_created":"2021-02-25T08:55:03Z"},{"scopus_import":"1","isi":1,"article_processing_charge":"Yes (via OA deal)","file":[{"date_updated":"2020-11-20T09:14:22Z","creator":"dernst","checksum":"f107e21b58f5930876f47144be37cf6c","content_type":"application/pdf","file_size":1897571,"file_id":"8779","relation":"main_file","access_level":"open_access","date_created":"2020-11-20T09:14:22Z","success":1,"file_name":"2020_ArchRatMechAn_Fischer.pdf"}],"volume":236,"quality_controlled":"1","citation":{"ieee":"J. L. Fischer and S. Hensel, “Weak–strong uniqueness for the Navier–Stokes equation for two fluids with surface tension,” Archive for Rational Mechanics and Analysis, vol. 236. Springer Nature, pp. 967–1087, 2020.","short":"J.L. Fischer, S. Hensel, Archive for Rational Mechanics and Analysis 236 (2020) 967–1087.","ista":"Fischer JL, Hensel S. 2020. Weak–strong uniqueness for the Navier–Stokes equation for two fluids with surface tension. Archive for Rational Mechanics and Analysis. 236, 967–1087.","chicago":"Fischer, Julian L, and Sebastian Hensel. “Weak–Strong Uniqueness for the Navier–Stokes Equation for Two Fluids with Surface Tension.” Archive for Rational Mechanics and Analysis. Springer Nature, 2020. https://doi.org/10.1007/s00205-019-01486-2.","mla":"Fischer, Julian L., and Sebastian Hensel. “Weak–Strong Uniqueness for the Navier–Stokes Equation for Two Fluids with Surface Tension.” Archive for Rational Mechanics and Analysis, vol. 236, Springer Nature, 2020, pp. 967–1087, doi:10.1007/s00205-019-01486-2.","ama":"Fischer JL, Hensel S. Weak–strong uniqueness for the Navier–Stokes equation for two fluids with surface tension. Archive for Rational Mechanics and Analysis. 2020;236:967-1087. doi:10.1007/s00205-019-01486-2","apa":"Fischer, J. L., & Hensel, S. (2020). Weak–strong uniqueness for the Navier–Stokes equation for two fluids with surface tension. Archive for Rational Mechanics and Analysis. Springer Nature. https://doi.org/10.1007/s00205-019-01486-2"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","doi":"10.1007/s00205-019-01486-2","date_updated":"2026-04-08T07:01:01Z","department":[{"_id":"JuFi"}],"has_accepted_license":"1","type":"journal_article","page":"967-1087","status":"public","publication":"Archive for Rational Mechanics and Analysis","date_published":"2020-05-01T00:00:00Z","ddc":["530","532"],"month":"05","file_date_updated":"2020-11-20T09:14:22Z","date_created":"2020-02-16T23:00:50Z","language":[{"iso":"eng"}],"day":"01","author":[{"first_name":"Julian L","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","last_name":"Fischer","orcid":"0000-0002-0479-558X","full_name":"Fischer, Julian L"},{"full_name":"Hensel, Sebastian","orcid":"0000-0001-7252-8072","id":"4D23B7DA-F248-11E8-B48F-1D18A9856A87","last_name":"Hensel","first_name":"Sebastian"}],"corr_author":"1","article_type":"original","related_material":{"record":[{"id":"10007","status":"public","relation":"dissertation_contains"}]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"project":[{"call_identifier":"H2020","grant_number":"665385","name":"International IST Doctoral Program","_id":"2564DBCA-B435-11E9-9278-68D0E5697425"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"publication_identifier":{"eissn":["1432-0673"],"issn":["0003-9527"]},"external_id":{"isi":["000511060200001"]},"publisher":"Springer Nature","title":"Weak–strong uniqueness for the Navier–Stokes equation for two fluids with surface tension","publication_status":"published","_id":"7489","oa_version":"Published Version","oa":1,"ec_funded":1,"intvolume":" 236","abstract":[{"lang":"eng","text":"In the present work, we consider the evolution of two fluids separated by a sharp interface in the presence of surface tension—like, for example, the evolution of oil bubbles in water. Our main result is a weak–strong uniqueness principle for the corresponding free boundary problem for the incompressible Navier–Stokes equation: as long as a strong solution exists, any varifold solution must coincide with it. In particular, in the absence of physical singularities, the concept of varifold solutions—whose global in time existence has been shown by Abels (Interfaces Free Bound 9(1):31–65, 2007) for general initial data—does not introduce a mechanism for non-uniqueness. The key ingredient of our approach is the construction of a relative entropy functional capable of controlling the interface error. If the viscosities of the two fluids do not coincide, even for classical (strong) solutions the gradient of the velocity field becomes discontinuous at the interface, introducing the need for a careful additional adaption of the relative entropy."}],"year":"2020"}]