[{"scopus_import":"1","publisher":"Society for Industrial and Applied Mathematics","language":[{"iso":"eng"}],"month":"07","article_type":"original","date_published":"2022-07-18T00:00:00Z","date_created":"2022-08-07T22:01:59Z","department":[{"_id":"JaMa"}],"intvolume":"        54","status":"public","day":"18","type":"journal_article","publication":"SIAM Journal on Mathematical Analysis","issue":"4","page":"4297-4333","title":"Evolutionary $\\Gamma$-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions","external_id":{"isi":["000889274600001"],"arxiv":["2008.10962"]},"doi":"10.1137/21M1410968","year":"2022","ec_funded":1,"related_material":{"record":[{"relation":"earlier_version","id":"10022","status":"public"}]},"isi":1,"main_file_link":[{"url":" https://doi.org/10.48550/arXiv.2008.10962","open_access":"1"}],"abstract":[{"lang":"eng","text":"We consider finite-volume approximations of Fokker--Planck equations on bounded convex domains in $\\mathbb{R}^d$ and study the corresponding gradient flow structures. We reprove the convergence of the discrete to continuous Fokker--Planck equation via the method of evolutionary $\\Gamma$-convergence, i.e., we pass to the limit at the level of the gradient flow structures, generalizing the one-dimensional result obtained by Disser and Liero. The proof is of variational nature and relies on a Mosco convergence result for functionals in the discrete-to-continuum limit that is of independent interest. Our results apply to arbitrary regular meshes, even though the associated discrete transport distances may fail to converge to the Wasserstein distance in this generality."}],"keyword":["Fokker--Planck equation","gradient flow","evolutionary $\\Gamma$-convergence"],"author":[{"id":"35C79D68-F248-11E8-B48F-1D18A9856A87","last_name":"Forkert","full_name":"Forkert, Dominik L","first_name":"Dominik L"},{"id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","first_name":"Jan","full_name":"Maas, Jan","last_name":"Maas","orcid":"0000-0002-0845-1338"},{"last_name":"Portinale","full_name":"Portinale, Lorenzo","first_name":"Lorenzo","id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87"}],"citation":{"ista":"Forkert DL, Maas J, Portinale L. 2022. Evolutionary $\\Gamma$-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions. SIAM Journal on Mathematical Analysis. 54(4), 4297–4333.","short":"D.L. Forkert, J. Maas, L. Portinale, SIAM Journal on Mathematical Analysis 54 (2022) 4297–4333.","mla":"Forkert, Dominik L., et al. “Evolutionary $\\Gamma$-Convergence of Entropic Gradient Flow Structures for Fokker-Planck Equations in Multiple Dimensions.” <i>SIAM Journal on Mathematical Analysis</i>, vol. 54, no. 4, Society for Industrial and Applied Mathematics, 2022, pp. 4297–333, doi:<a href=\"https://doi.org/10.1137/21M1410968\">10.1137/21M1410968</a>.","ama":"Forkert DL, Maas J, Portinale L. Evolutionary $\\Gamma$-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions. <i>SIAM Journal on Mathematical Analysis</i>. 2022;54(4):4297-4333. doi:<a href=\"https://doi.org/10.1137/21M1410968\">10.1137/21M1410968</a>","chicago":"Forkert, Dominik L, Jan Maas, and Lorenzo Portinale. “Evolutionary $\\Gamma$-Convergence of Entropic Gradient Flow Structures for Fokker-Planck Equations in Multiple Dimensions.” <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial and Applied Mathematics, 2022. <a href=\"https://doi.org/10.1137/21M1410968\">https://doi.org/10.1137/21M1410968</a>.","apa":"Forkert, D. L., Maas, J., &#38; Portinale, L. (2022). Evolutionary $\\Gamma$-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions. <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/21M1410968\">https://doi.org/10.1137/21M1410968</a>","ieee":"D. L. Forkert, J. Maas, and L. Portinale, “Evolutionary $\\Gamma$-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions,” <i>SIAM Journal on Mathematical Analysis</i>, vol. 54, no. 4. Society for Industrial and Applied Mathematics, pp. 4297–4333, 2022."},"publication_status":"published","publication_identifier":{"eissn":["1095-7154"],"issn":["0036-1410"]},"_id":"11739","project":[{"call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117"},{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"},{"_id":"260788DE-B435-11E9-9278-68D0E5697425","name":"Dissipation and Dispersion in Nonlinear Partial Differential Equations","call_identifier":"FWF"}],"quality_controlled":"1","oa_version":"Preprint","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","acknowledgement":"This work was supported by the European Research Council (ERC) under the European Union's Horizon 2020 Research and Innovation Programme grant 716117 and by the AustrianScience Fund (FWF) through grants F65 and W1245.","arxiv":1,"article_processing_charge":"No","volume":54,"date_updated":"2023-08-03T12:37:21Z","oa":1},{"quality_controlled":"1","oa_version":"Preprint","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_identifier":{"eissn":["1095-7154"],"issn":["0036-1410"]},"_id":"12305","article_processing_charge":"No","date_updated":"2023-08-04T10:34:56Z","oa":1,"volume":54,"arxiv":1,"author":[{"last_name":"Abels","full_name":"Abels, Helmut","first_name":"Helmut"},{"last_name":"Moser","full_name":"Moser, Maximilian","first_name":"Maximilian","id":"a60047a9-da77-11eb-85b4-c4dc385ebb8c"}],"keyword":["Applied Mathematics","Computational Mathematics","Analysis"],"abstract":[{"lang":"eng","text":"This paper is concerned with the sharp interface limit for the Allen--Cahn equation with a nonlinear Robin boundary condition in a bounded smooth domain Ω⊂\\R2. We assume that a diffuse interface already has developed and that it is in contact with the boundary ∂Ω. The boundary condition is designed in such a way that the limit problem is given by the mean curvature flow with constant α-contact angle. For α close to 90° we prove a local in time convergence result for well-prepared initial data for times when a smooth solution to the limit problem exists. Based on the latter we construct a suitable curvilinear coordinate system and carry out a rigorous asymptotic expansion for the Allen--Cahn equation with the nonlinear Robin boundary condition. Moreover, we show a spectral estimate for the corresponding linearized Allen--Cahn operator and with its aid we derive strong norm estimates for the difference of the exact and approximate solutions using a Gronwall-type argument."}],"citation":{"ama":"Abels H, Moser M. Convergence of the Allen--Cahn equation with a nonlinear Robin boundary condition to mean curvature flow with contact angle close to 90°. <i>SIAM Journal on Mathematical Analysis</i>. 2022;54(1):114-172. doi:<a href=\"https://doi.org/10.1137/21m1424925\">10.1137/21m1424925</a>","mla":"Abels, Helmut, and Maximilian Moser. “Convergence of the Allen--Cahn Equation with a Nonlinear Robin Boundary Condition to Mean Curvature Flow with Contact Angle Close to 90°.” <i>SIAM Journal on Mathematical Analysis</i>, vol. 54, no. 1, Society for Industrial and Applied Mathematics, 2022, pp. 114–72, doi:<a href=\"https://doi.org/10.1137/21m1424925\">10.1137/21m1424925</a>.","ista":"Abels H, Moser M. 2022. Convergence of the Allen--Cahn equation with a nonlinear Robin boundary condition to mean curvature flow with contact angle close to 90°. SIAM Journal on Mathematical Analysis. 54(1), 114–172.","short":"H. Abels, M. Moser, SIAM Journal on Mathematical Analysis 54 (2022) 114–172.","apa":"Abels, H., &#38; Moser, M. (2022). Convergence of the Allen--Cahn equation with a nonlinear Robin boundary condition to mean curvature flow with contact angle close to 90°. <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/21m1424925\">https://doi.org/10.1137/21m1424925</a>","ieee":"H. Abels and M. Moser, “Convergence of the Allen--Cahn equation with a nonlinear Robin boundary condition to mean curvature flow with contact angle close to 90°,” <i>SIAM Journal on Mathematical Analysis</i>, vol. 54, no. 1. Society for Industrial and Applied Mathematics, pp. 114–172, 2022.","chicago":"Abels, Helmut, and Maximilian Moser. “Convergence of the Allen--Cahn Equation with a Nonlinear Robin Boundary Condition to Mean Curvature Flow with Contact Angle Close to 90°.” <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial and Applied Mathematics, 2022. <a href=\"https://doi.org/10.1137/21m1424925\">https://doi.org/10.1137/21m1424925</a>."},"publication_status":"published","isi":1,"main_file_link":[{"open_access":"1","url":" https://doi.org/10.48550/arXiv.2105.08434"}],"title":"Convergence of the Allen--Cahn equation with a nonlinear Robin boundary condition to mean curvature flow with contact angle close to 90°","external_id":{"isi":["000762768000004"],"arxiv":["2105.08434"]},"doi":"10.1137/21m1424925","year":"2022","page":"114-172","publication":"SIAM Journal on Mathematical Analysis","issue":"1","status":"public","intvolume":"        54","type":"journal_article","day":"04","date_created":"2023-01-16T10:07:00Z","department":[{"_id":"JuFi"}],"language":[{"iso":"eng"}],"scopus_import":"1","publisher":"Society for Industrial and Applied Mathematics","date_published":"2022-01-04T00:00:00Z","article_type":"original","month":"01"},{"page":"605-622","issue":"1","publication":"SIAM Journal on Mathematical Analysis","type":"journal_article","day":"12","status":"public","intvolume":"        52","department":[{"_id":"RoSe"}],"license":"https://creativecommons.org/licenses/by-nc-nd/4.0/","has_accepted_license":"1","date_created":"2021-08-06T07:34:16Z","date_published":"2020-02-12T00:00:00Z","article_type":"original","month":"02","language":[{"iso":"eng"}],"publisher":"Society for Industrial & Applied Mathematics ","scopus_import":"1","oa":1,"date_updated":"2023-09-07T13:30:11Z","volume":52,"article_processing_charge":"No","arxiv":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","acknowledgement":"We are grateful for the hospitality at the Mittag-Leffler Institute, where part of this work has been done. The work of the authors was supported by the European Research Council (ERC)under the European Union's Horizon 2020 research and innovation programme grant 694227.","quality_controlled":"1","oa_version":"Preprint","project":[{"grant_number":"694227","call_identifier":"H2020","name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"}],"_id":"9781","publication_identifier":{"issn":["0036-1410"],"eissn":["1095-7154"]},"publication_status":"published","citation":{"chicago":"Feliciangeli, Dario, and Robert Seiringer. “Uniqueness and Nondegeneracy of Minimizers of the Pekar Functional on a Ball.” <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial &#38; Applied Mathematics , 2020. <a href=\"https://doi.org/10.1137/19m126284x\">https://doi.org/10.1137/19m126284x</a>.","ieee":"D. Feliciangeli and R. Seiringer, “Uniqueness and nondegeneracy of minimizers of the Pekar functional on a ball,” <i>SIAM Journal on Mathematical Analysis</i>, vol. 52, no. 1. Society for Industrial &#38; Applied Mathematics , pp. 605–622, 2020.","apa":"Feliciangeli, D., &#38; Seiringer, R. (2020). Uniqueness and nondegeneracy of minimizers of the Pekar functional on a ball. <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial &#38; Applied Mathematics . <a href=\"https://doi.org/10.1137/19m126284x\">https://doi.org/10.1137/19m126284x</a>","short":"D. Feliciangeli, R. Seiringer, SIAM Journal on Mathematical Analysis 52 (2020) 605–622.","ista":"Feliciangeli D, Seiringer R. 2020. Uniqueness and nondegeneracy of minimizers of the Pekar functional on a ball. SIAM Journal on Mathematical Analysis. 52(1), 605–622.","mla":"Feliciangeli, Dario, and Robert Seiringer. “Uniqueness and Nondegeneracy of Minimizers of the Pekar Functional on a Ball.” <i>SIAM Journal on Mathematical Analysis</i>, vol. 52, no. 1, Society for Industrial &#38; Applied Mathematics , 2020, pp. 605–22, doi:<a href=\"https://doi.org/10.1137/19m126284x\">10.1137/19m126284x</a>.","ama":"Feliciangeli D, Seiringer R. Uniqueness and nondegeneracy of minimizers of the Pekar functional on a ball. <i>SIAM Journal on Mathematical Analysis</i>. 2020;52(1):605-622. doi:<a href=\"https://doi.org/10.1137/19m126284x\">10.1137/19m126284x</a>"},"author":[{"id":"41A639AA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-0754-8530","full_name":"Feliciangeli, Dario","last_name":"Feliciangeli","first_name":"Dario"},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","last_name":"Seiringer","full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521"}],"keyword":["Applied Mathematics","Computational Mathematics","Analysis"],"abstract":[{"text":"We consider the Pekar functional on a ball in ℝ3. We prove uniqueness of minimizers, and a quadratic lower bound in terms of the distance to the minimizer. The latter follows from nondegeneracy of the Hessian at the minimum.","lang":"eng"}],"main_file_link":[{"url":"https://arxiv.org/abs/1904.08647","open_access":"1"}],"isi":1,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","image":"/images/cc_by_nc_nd.png","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","short":"CC BY-NC-ND (4.0)"},"ddc":["510"],"related_material":{"record":[{"status":"public","id":"9733","relation":"dissertation_contains"}]},"ec_funded":1,"doi":"10.1137/19m126284x","year":"2020","external_id":{"arxiv":["1904.08647 "],"isi":["000546967700022"]},"title":"Uniqueness and nondegeneracy of minimizers of the Pekar functional on a ball"}]