Obstacle problems for integro-differential operators: Higher regularity of free boundaries

We study the higher regularity of free boundaries in obstacle problems for integrodifferential operators. Our main result establishes that, once free boundaries are $C^{1, \alpha}$, then they are $C^{\infty}$. This completes the study of regular points, initiated in [5]. In order to achieve this, we...

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Detalles Bibliográficos
Autores: Abatangelo, Nicola, Ros, Xavier
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2020
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2445/194137
Acceso en línea:https://hdl.handle.net/2445/194137
Access Level:acceso abierto
Palabra clave:Operadors integrals
Operadors diferencials
Teoria d'operadors
Equacions en derivades parcials
Integral operators
Differential operators
Operator theory
Partial differential equations
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spelling Obstacle problems for integro-differential operators: Higher regularity of free boundariesAbatangelo, NicolaRos, XavierOperadors integralsOperadors diferencialsTeoria d'operadorsEquacions en derivades parcialsIntegral operatorsDifferential operatorsOperator theoryPartial differential equationsWe study the higher regularity of free boundaries in obstacle problems for integrodifferential operators. Our main result establishes that, once free boundaries are $C^{1, \alpha}$, then they are $C^{\infty}$. This completes the study of regular points, initiated in [5]. In order to achieve this, we need to establish optimal boundary regularity estimates for solutions to linear nonlocal equations in $C^{k, \alpha}$ domains. These new estimates are the core of our paper, and extend previously known results by Grubb (for $k=\infty$ ) and by the second author and Serra (for $k=1$ ).Elsevier B.V.2023202320202023info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttps://hdl.handle.net/2445/194137Articles publicats en revistes (Matemàtiques i Informàtica)reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésVersió postprint del document publicat a: https://doi.org/10.1016/j.aim.2019.106931Advances in Mathematics, 2020, vol. 360, num. Article 106931, p. 106931https://doi.org/10.1016/j.aim.2019.106931cc-by-nc-nd (c) Elsevier B.V., 2020https://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:recercat.cat:2445/1941372026-05-29T05:05:01Z
dc.title.none.fl_str_mv Obstacle problems for integro-differential operators: Higher regularity of free boundaries
title Obstacle problems for integro-differential operators: Higher regularity of free boundaries
spellingShingle Obstacle problems for integro-differential operators: Higher regularity of free boundaries
Abatangelo, Nicola
Operadors integrals
Operadors diferencials
Teoria d'operadors
Equacions en derivades parcials
Integral operators
Differential operators
Operator theory
Partial differential equations
title_short Obstacle problems for integro-differential operators: Higher regularity of free boundaries
title_full Obstacle problems for integro-differential operators: Higher regularity of free boundaries
title_fullStr Obstacle problems for integro-differential operators: Higher regularity of free boundaries
title_full_unstemmed Obstacle problems for integro-differential operators: Higher regularity of free boundaries
title_sort Obstacle problems for integro-differential operators: Higher regularity of free boundaries
dc.creator.none.fl_str_mv Abatangelo, Nicola
Ros, Xavier
author Abatangelo, Nicola
author_facet Abatangelo, Nicola
Ros, Xavier
author_role author
author2 Ros, Xavier
author2_role author
dc.subject.none.fl_str_mv Operadors integrals
Operadors diferencials
Teoria d'operadors
Equacions en derivades parcials
Integral operators
Differential operators
Operator theory
Partial differential equations
topic Operadors integrals
Operadors diferencials
Teoria d'operadors
Equacions en derivades parcials
Integral operators
Differential operators
Operator theory
Partial differential equations
description We study the higher regularity of free boundaries in obstacle problems for integrodifferential operators. Our main result establishes that, once free boundaries are $C^{1, \alpha}$, then they are $C^{\infty}$. This completes the study of regular points, initiated in [5]. In order to achieve this, we need to establish optimal boundary regularity estimates for solutions to linear nonlocal equations in $C^{k, \alpha}$ domains. These new estimates are the core of our paper, and extend previously known results by Grubb (for $k=\infty$ ) and by the second author and Serra (for $k=1$ ).
publishDate 2020
dc.date.none.fl_str_mv 2020
2023
2023
2023
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/194137
url https://hdl.handle.net/2445/194137
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Versió postprint del document publicat a: https://doi.org/10.1016/j.aim.2019.106931
Advances in Mathematics, 2020, vol. 360, num. Article 106931, p. 106931
https://doi.org/10.1016/j.aim.2019.106931
dc.rights.none.fl_str_mv cc-by-nc-nd (c) Elsevier B.V., 2020
https://creativecommons.org/licenses/by-nc-nd/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv cc-by-nc-nd (c) Elsevier B.V., 2020
https://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier B.V.
publisher.none.fl_str_mv Elsevier B.V.
dc.source.none.fl_str_mv Articles publicats en revistes (Matemàtiques i Informàtica)
reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.81155

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