{"tmp":{"short":"CC BY (4.0)","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)"},"file_date_updated":"2023-10-04T11:34:10Z","oa_version":"Published Version","has_accepted_license":"1","oa":1,"abstract":[{"lang":"eng","text":"This paper deals with the large-scale behaviour of dynamical optimal transport on Zd\r\n-periodic graphs with general lower semicontinuous and convex energy densities. Our main contribution is a homogenisation result that describes the effective behaviour of the discrete problems in terms of a continuous optimal transport problem. The effective energy density can be explicitly expressed in terms of a cell formula, which is a finite-dimensional convex programming problem that depends non-trivially on the local geometry of the discrete graph and the discrete energy density. Our homogenisation result is derived from a Γ\r\n-convergence result for action functionals on curves of measures, which we prove under very mild growth conditions on the energy density. We investigate the cell formula in several cases of interest, including finite-volume discretisations of the Wasserstein distance, where non-trivial limiting behaviour occurs."}],"publisher":"Springer Nature","article_type":"original","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","volume":62,"day":"28","intvolume":"        62","date_updated":"2023-10-04T11:34:49Z","scopus_import":"1","article_processing_charge":"Yes (via OA deal)","quality_controlled":"1","article_number":"143","date_published":"2023-04-28T00:00:00Z","department":[{"_id":"JaMa"}],"month":"04","doi":"10.1007/s00526-023-02472-z","publication_identifier":{"issn":["0944-2669"],"eissn":["1432-0835"]},"publication":"Calculus of Variations and Partial Differential Equations","isi":1,"external_id":{"arxiv":["2110.15321"],"isi":["000980588900001"]},"title":"Homogenisation of dynamical optimal transport on periodic graphs","type":"journal_article","year":"2023","status":"public","file":[{"file_name":"2023_CalculusEquations_Gladbach.pdf","access_level":"open_access","file_id":"14393","creator":"dernst","date_updated":"2023-10-04T11:34:10Z","date_created":"2023-10-04T11:34:10Z","file_size":1240995,"relation":"main_file","content_type":"application/pdf","success":1,"checksum":"359bee38d94b7e0aa73925063cb8884d"}],"citation":{"ieee":"P. Gladbach, E. Kopfer, J. Maas, and L. Portinale, “Homogenisation of dynamical optimal transport on periodic graphs,” <i>Calculus of Variations and Partial Differential Equations</i>, vol. 62, no. 5. Springer Nature, 2023.","short":"P. Gladbach, E. Kopfer, J. Maas, L. Portinale, Calculus of Variations and Partial Differential Equations 62 (2023).","ama":"Gladbach P, Kopfer E, Maas J, Portinale L. Homogenisation of dynamical optimal transport on periodic graphs. <i>Calculus of Variations and Partial Differential Equations</i>. 2023;62(5). doi:<a href=\"https://doi.org/10.1007/s00526-023-02472-z\">10.1007/s00526-023-02472-z</a>","apa":"Gladbach, P., Kopfer, E., Maas, J., &#38; Portinale, L. (2023). Homogenisation of dynamical optimal transport on periodic graphs. <i>Calculus of Variations and Partial Differential Equations</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00526-023-02472-z\">https://doi.org/10.1007/s00526-023-02472-z</a>","chicago":"Gladbach, Peter, Eva Kopfer, Jan Maas, and Lorenzo Portinale. “Homogenisation of Dynamical Optimal Transport on Periodic Graphs.” <i>Calculus of Variations and Partial Differential Equations</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00526-023-02472-z\">https://doi.org/10.1007/s00526-023-02472-z</a>.","ista":"Gladbach P, Kopfer E, Maas J, Portinale L. 2023. Homogenisation of dynamical optimal transport on periodic graphs. Calculus of Variations and Partial Differential Equations. 62(5), 143.","mla":"Gladbach, Peter, et al. “Homogenisation of Dynamical Optimal Transport on Periodic Graphs.” <i>Calculus of Variations and Partial Differential Equations</i>, vol. 62, no. 5, 143, Springer Nature, 2023, doi:<a href=\"https://doi.org/10.1007/s00526-023-02472-z\">10.1007/s00526-023-02472-z</a>."},"acknowledgement":"J.M. gratefully acknowledges support by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 716117). J.M and L.P. also acknowledge support from the Austrian Science Fund (FWF), grants No F65 and W1245. E.K. gratefully acknowledges support by the German Research Foundation through the Hausdorff Center for Mathematics and the Collaborative Research Center 1060. P.G. is partially funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—350398276. We thank the anonymous reviewer for the careful reading and for useful suggestions. Open access funding provided by Austrian Science Fund (FWF).","project":[{"grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics"},{"grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"},{"call_identifier":"FWF","name":"Dissipation and Dispersion in Nonlinear Partial Differential Equations","_id":"260788DE-B435-11E9-9278-68D0E5697425"}],"_id":"12959","ec_funded":1,"date_created":"2023-05-14T22:01:00Z","issue":"5","language":[{"iso":"eng"}],"ddc":["510"],"author":[{"last_name":"Gladbach","first_name":"Peter","full_name":"Gladbach, Peter"},{"full_name":"Kopfer, Eva","last_name":"Kopfer","first_name":"Eva"},{"last_name":"Maas","first_name":"Jan","full_name":"Maas, Jan","orcid":"0000-0002-0845-1338","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87"},{"id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87","first_name":"Lorenzo","last_name":"Portinale","full_name":"Portinale, Lorenzo"}],"publication_status":"published"}