[{"status":"public","department":[{"_id":"JaMa"}],"has_accepted_license":"1","month":"01","language":[{"iso":"eng"}],"fulldoi":"https://doi.org/10.1007/s11118-025-10251-y","abstract":[{"text":"We characterize all semigroups sandwiched between the semigroup of a Dirichlet form and the semigroup of its active main part. In case the Dirichlet form is regular, we give a more explicit description of the quadratic forms of the sandwiched semigroups in terms of pairs consisting of an open set and a measure on an abstract boundary.","lang":"eng"}],"date_updated":"2026-07-27T10:25:46Z","day":"01","volume":64,"date_created":"2025-12-14T23:02:03Z","article_processing_charge":"Yes (via OA deal)","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","publication_identifier":{"issn":["0926-2601"],"eissn":["1572-929X"]},"title":"Boundary representations of intermediate forms between a regular Dirichlet form and its active main part","date_published":"2026-01-01T00:00:00Z","arxiv":1,"file_date_updated":"2026-07-27T10:25:21Z","publication":"Potential Analysis","scopus_import":"1","author":[{"last_name":"Keller","first_name":"Matthias","full_name":"Keller, Matthias"},{"last_name":"Lenz","full_name":"Lenz, Daniel","first_name":"Daniel"},{"last_name":"Schmidt","first_name":"Marcel","full_name":"Schmidt, Marcel"},{"first_name":"Michael","last_name":"Schwarz","full_name":"Schwarz, Michael"},{"full_name":"Wirth, Melchior","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","first_name":"Melchior","last_name":"Wirth","orcid":"0000-0002-0519-4241"}],"external_id":{"arxiv":["2301.01035"]},"_id":"20814","dataavailabilitystatement":"No datasets were generated or analysed during the current study.","acknowledgement":"Open Access funding enabled and organized by Projekt DEAL. The first three authors acknowledge financial support of the DFG within the priority programme Geometry at Infinity.\r\nM.W. acknowledges financial support by the German Academic Scholarship Foundation, by the Austrian Science Fund (FWF) through grant number F65 and the Esprit Programme [ESP 156], and by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 716117).","oa_version":"Published Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Keller, Matthias, et al. “Boundary Representations of Intermediate Forms between a Regular Dirichlet Form and Its Active Main Part.” <i>Potential Analysis</i>, vol. 64, no. 1, 6, Springer Nature, 2026, doi:<a href=\"https://doi.org/10.1007/s11118-025-10251-y\">10.1007/s11118-025-10251-y</a>.","chicago":"Keller, Matthias, Daniel Lenz, Marcel Schmidt, Michael Schwarz, and Melchior Wirth. “Boundary Representations of Intermediate Forms between a Regular Dirichlet Form and Its Active Main Part.” <i>Potential Analysis</i>. Springer Nature, 2026. <a href=\"https://doi.org/10.1007/s11118-025-10251-y\">https://doi.org/10.1007/s11118-025-10251-y</a>.","ieee":"M. Keller, D. Lenz, M. Schmidt, M. Schwarz, and M. Wirth, “Boundary representations of intermediate forms between a regular Dirichlet form and its active main part,” <i>Potential Analysis</i>, vol. 64, no. 1. Springer Nature, 2026.","apa":"Keller, M., Lenz, D., Schmidt, M., Schwarz, M., &#38; Wirth, M. (2026). Boundary representations of intermediate forms between a regular Dirichlet form and its active main part. <i>Potential Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11118-025-10251-y\">https://doi.org/10.1007/s11118-025-10251-y</a>","ista":"Keller M, Lenz D, Schmidt M, Schwarz M, Wirth M. 2026. Boundary representations of intermediate forms between a regular Dirichlet form and its active main part. Potential Analysis. 64(1), 6.","ama":"Keller M, Lenz D, Schmidt M, Schwarz M, Wirth M. Boundary representations of intermediate forms between a regular Dirichlet form and its active main part. <i>Potential Analysis</i>. 2026;64(1). doi:<a href=\"https://doi.org/10.1007/s11118-025-10251-y\">10.1007/s11118-025-10251-y</a>","short":"M. Keller, D. Lenz, M. Schmidt, M. Schwarz, M. Wirth, Potential Analysis 64 (2026)."},"publication_status":"published","PlanS_conform":"1","researchdata_availability":"no","ec_funded":1,"doi":"10.1007/s11118-025-10251-y","year":"2026","quality_controlled":"1","ddc":["510"],"publisher":"Springer Nature","issue":"1","intvolume":"        64","OA_type":"hybrid","keyword":["Dirichlet forms","Domination of semigroups","Dirichlet","Neumann and Robin boundary conditions"],"file":[{"date_created":"2026-07-27T10:25:21Z","file_size":445935,"relation":"main_file","content_type":"application/pdf","success":1,"creator":"dernst","access_level":"open_access","checksum":"9f5a4e900b8d4c74c6b5bf7c3bad54e1","file_id":"22414","date_updated":"2026-07-27T10:25:21Z","file_name":"2026_PotentialAnalysis_Keller.pdf"}],"supplementarymaterial":"no","article_number":"6","mathsc":["31C15","31C25","35A15","35J10","47D07"],"article_type":"original","OA_place":"publisher","das_tickbox":"1","project":[{"name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504"},{"name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"name":"Gradient flow techniques for quantum Markov semigroups","_id":"34c6ea2d-11ca-11ed-8bc3-c04f3c502833","grant_number":"ESP156_N"}],"oa":1},{"publisher":"Texas State University","issue":"118","intvolume":"      2005","OA_type":"green","extern":"1","mathsc":["35J10"],"article_type":"original","OA_place":"repository","oa":1,"das_tickbox":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Tao, Terence, and Monica Vişan. “Stability of Energy-Critical Nonlinear Schrodinger Equations in High Dimensions.” <i>Electronic Journal of Differential Equations</i>, vol. 2005, no. 118, Texas State University, 2005, pp. 1–28.","chicago":"Tao, Terence, and Monica Vişan. “Stability of Energy-Critical Nonlinear Schrodinger Equations in High Dimensions.” <i>Electronic Journal of Differential Equations</i>. Texas State University, 2005.","apa":"Tao, T., &#38; Vişan, M. (2005). Stability of energy-critical nonlinear Schrodinger equations in high dimensions. <i>Electronic Journal of Differential Equations</i>. Texas State University.","ieee":"T. Tao and M. Vişan, “Stability of energy-critical nonlinear Schrodinger equations in high dimensions,” <i>Electronic Journal of Differential Equations</i>, vol. 2005, no. 118. Texas State University, pp. 1–28, 2005.","ista":"Tao T, Vişan M. 2005. Stability of energy-critical nonlinear Schrodinger equations in high dimensions. Electronic Journal of Differential Equations. 2005(118), 1–28.","short":"T. Tao, M. Vişan, Electronic Journal of Differential Equations 2005 (2005) 1–28.","ama":"Tao T, Vişan M. Stability of energy-critical nonlinear Schrodinger equations in high dimensions. <i>Electronic Journal of Differential Equations</i>. 2005;2005(118):1-28."},"publication_status":"published","page":"1-28","year":"2005","quality_controlled":"1","publication_identifier":{"eissn":["1550-6150"]},"title":"Stability of energy-critical nonlinear Schrodinger equations in high dimensions","arxiv":1,"date_published":"2005-10-26T00:00:00Z","publication":"Electronic Journal of Differential Equations","scopus_import":"1","author":[{"last_name":"Tao","full_name":"Tao, Terence","first_name":"Terence"},{"last_name":"Visan","full_name":"Visan, Monica","first_name":"Monica","id":"056daca0-b8d1-11f0-964f-f91054abf8ca"}],"external_id":{"arxiv":["math/0507005"]},"_id":"22086","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.math/0507005","open_access":"1"}],"oa_version":"Preprint","status":"public","language":[{"iso":"eng"}],"month":"10","abstract":[{"text":"We develop the existence, uniqueness, continuity, stability, and scattering theory for energy-critical nonlinear Schrödinger equations in dimensions n ≥ 3, for solutions which have large, but finite, energy and large, but finite, Strichartz norms. For dimensions n ≤ 6, this theory is a standard extension of the small data well-posedness theory based on iteration in Strichartz spaces. However, in dimensions n > 6 there is an obstruction to this approach because of the subquadratic nature of the nonlinearity (which makes the derivative of the nonlinearity non-Lipschitz). We resolve this by iterating in exotic Strichartz spaces instead. The theory developed here will be applied in a subsequent paper of the second author, [21], to establish global well-posedness and scattering for the defocusing energy-critical equation for large energy data.","lang":"eng"}],"day":"26","date_updated":"2026-07-01T12:31:43Z","volume":2005,"date_created":"2026-06-19T08:44:06Z","type":"journal_article","article_processing_charge":"No"}]