Semiconvexity estimates for nonlinear integro-differential equations

In this paper we establish for the first time local semiconvexity estimates for fully nonlinear equations and for obstacle problems driven by integro-differential operators with general kernels. Our proof is based on the Bernstein technique, which we develop for a natural class of nonlocal operators...

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Detalles Bibliográficos
Autores: Ros, Xavier, Torres Latorre, Clara, Weidner, Marvin
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2025
País:España
Institución:Universidad de Oviedo (UNIOVI)
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:dnet:ubarcelona__::350535579a71761fd9781a261858a995
Acceso en línea:https://hdl.handle.net/2445/229554
Access Level:acceso abierto
Palabra clave:Teoria d&apos
operadors
Equacions en derivades parcials
Teoria del potencial (Matemàtica)
Processos de Markov
Operator theory
Partial differential equations
Potential theory (Mathematics)
Markov processes
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spelling Semiconvexity estimates for nonlinear integro-differential equationsRos, XavierTorres Latorre, ClaraWeidner, MarvinTeoria d&aposoperadorsEquacions en derivades parcialsTeoria del potencial (Matemàtica)Processos de MarkovOperator theoryPartial differential equationsPotential theory (Mathematics)Markov processesIn this paper we establish for the first time local semiconvexity estimates for fully nonlinear equations and for obstacle problems driven by integro-differential operators with general kernels. Our proof is based on the Bernstein technique, which we develop for a natural class of nonlocal operators and consider to be of independent interest. In particular, we solve an open problem from Cabré-Dipierro-Valdinoci. As an application of our result, we establish optimal regularity estimates and smoothness of the free boundary near regular points for the nonlocal obstacle problem on domains. Finally, we also extend the Bernstein technique to parabolic equations and nonsymmetric operators.Wiley2025info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://hdl.handle.net/2445/229554Articles publicats en revistes (Matemàtiques i Informàtica)reponame:Dipòsit Digital de la UBinstname:Universidad de Oviedo (UNIOVI)InglésReproducció del document publicat a: https://doi.org/10.1002/cpa.22237Communications on Pure and Applied Mathematics, 2025, vol. 78, num.3, p. 592-647https://doi.org/10.1002/cpa.22237cc by (c) Ros, Xavier et al., 2025http://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:dnet:ubarcelona__::350535579a71761fd9781a261858a9952026-05-27T06:46:51Z
dc.title.none.fl_str_mv Semiconvexity estimates for nonlinear integro-differential equations
title Semiconvexity estimates for nonlinear integro-differential equations
spellingShingle Semiconvexity estimates for nonlinear integro-differential equations
Ros, Xavier
Teoria d&apos
operadors
Equacions en derivades parcials
Teoria del potencial (Matemàtica)
Processos de Markov
Operator theory
Partial differential equations
Potential theory (Mathematics)
Markov processes
title_short Semiconvexity estimates for nonlinear integro-differential equations
title_full Semiconvexity estimates for nonlinear integro-differential equations
title_fullStr Semiconvexity estimates for nonlinear integro-differential equations
title_full_unstemmed Semiconvexity estimates for nonlinear integro-differential equations
title_sort Semiconvexity estimates for nonlinear integro-differential equations
dc.creator.none.fl_str_mv Ros, Xavier
Torres Latorre, Clara
Weidner, Marvin
author Ros, Xavier
author_facet Ros, Xavier
Torres Latorre, Clara
Weidner, Marvin
author_role author
author2 Torres Latorre, Clara
Weidner, Marvin
author2_role author
author
dc.subject.none.fl_str_mv Teoria d&apos
operadors
Equacions en derivades parcials
Teoria del potencial (Matemàtica)
Processos de Markov
Operator theory
Partial differential equations
Potential theory (Mathematics)
Markov processes
topic Teoria d&apos
operadors
Equacions en derivades parcials
Teoria del potencial (Matemàtica)
Processos de Markov
Operator theory
Partial differential equations
Potential theory (Mathematics)
Markov processes
description In this paper we establish for the first time local semiconvexity estimates for fully nonlinear equations and for obstacle problems driven by integro-differential operators with general kernels. Our proof is based on the Bernstein technique, which we develop for a natural class of nonlocal operators and consider to be of independent interest. In particular, we solve an open problem from Cabré-Dipierro-Valdinoci. As an application of our result, we establish optimal regularity estimates and smoothness of the free boundary near regular points for the nonlocal obstacle problem on domains. Finally, we also extend the Bernstein technique to parabolic equations and nonsymmetric operators.
publishDate 2025
dc.date.none.fl_str_mv 2025
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/229554
url https://hdl.handle.net/2445/229554
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Reproducció del document publicat a: https://doi.org/10.1002/cpa.22237
Communications on Pure and Applied Mathematics, 2025, vol. 78, num.3, p. 592-647
https://doi.org/10.1002/cpa.22237
dc.rights.none.fl_str_mv cc by (c) Ros, Xavier et al., 2025
http://creativecommons.org/licenses/by/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv cc by (c) Ros, Xavier et al., 2025
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Wiley
publisher.none.fl_str_mv Wiley
dc.source.none.fl_str_mv Articles publicats en revistes (Matemàtiques i Informàtica)
reponame:Dipòsit Digital de la UB
instname:Universidad de Oviedo (UNIOVI)
instname_str Universidad de Oviedo (UNIOVI)
reponame_str Dipòsit Digital de la UB
collection Dipòsit Digital de la UB
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,812429

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