Regularity of flat free boundaries for two-phase p(x)-Laplacian problems with right hand side

Autores
Ferrari, Fausto; Lederman, Claudia Beatriz
Año de publicación
2024
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We consider viscosity solutions to two-phase free boundary problems for the p(x)-Laplacian with non-zero right hand side. We prove that flat free boundaries are C1,γ . No assumption on the Lipschitz continuity of solutions is made. These regularity results are the first ones in literature for two-phase free boundary problems for the p(x)-Laplacian and also for twophase problems for singular/degenerate operators with non-zero right hand side. They are new even when p(x) ≡ p, i.e., for the p-Laplacian. The fact that our results hold for merely viscosity solutions allows a wide applicability.
Fil: Ferrari, Fausto. Universidad de Bologna; Italia
Fil: Lederman, Claudia Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Materia
FREE BOUNDARY PROBLEM
SINGULAR / DEGENERATE OPERATOR
REGULARITY
VISCOSITY SOLUTIONS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/265089
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Regularity of flat free boundaries for two-phase p(x)-Laplacian problems with right hand sideFerrari, FaustoLederman, Claudia BeatrizFREE BOUNDARY PROBLEMSINGULAR / DEGENERATE OPERATORREGULARITYVISCOSITY SOLUTIONShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We consider viscosity solutions to two-phase free boundary problems for the p(x)-Laplacian with non-zero right hand side. We prove that flat free boundaries are C1,γ . No assumption on the Lipschitz continuity of solutions is made. These regularity results are the first ones in literature for two-phase free boundary problems for the p(x)-Laplacian and also for twophase problems for singular/degenerate operators with non-zero right hand side. They are new even when p(x) ≡ p, i.e., for the p-Laplacian. The fact that our results hold for merely viscosity solutions allows a wide applicability.Fil: Ferrari, Fausto. Universidad de Bologna; ItaliaFil: Lederman, Claudia Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaSpringer2024-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/265089Ferrari, Fausto; Lederman, Claudia Beatriz; Regularity of flat free boundaries for two-phase p(x)-Laplacian problems with right hand side; Springer; Calculus Of Variations And Partial Differential Equations; 63; 5; 5-2024; 1-430944-26691432-0835CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/10.1007/s00526-024-02741-5info:eu-repo/semantics/altIdentifier/doi/10.1007/s00526-024-02741-5info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:47:03Zoai:ri.conicet.gov.ar:11336/265089instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-22 11:47:03.934CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Regularity of flat free boundaries for two-phase p(x)-Laplacian problems with right hand side
title Regularity of flat free boundaries for two-phase p(x)-Laplacian problems with right hand side
spellingShingle Regularity of flat free boundaries for two-phase p(x)-Laplacian problems with right hand side
Ferrari, Fausto
FREE BOUNDARY PROBLEM
SINGULAR / DEGENERATE OPERATOR
REGULARITY
VISCOSITY SOLUTIONS
title_short Regularity of flat free boundaries for two-phase p(x)-Laplacian problems with right hand side
title_full Regularity of flat free boundaries for two-phase p(x)-Laplacian problems with right hand side
title_fullStr Regularity of flat free boundaries for two-phase p(x)-Laplacian problems with right hand side
title_full_unstemmed Regularity of flat free boundaries for two-phase p(x)-Laplacian problems with right hand side
title_sort Regularity of flat free boundaries for two-phase p(x)-Laplacian problems with right hand side
dc.creator.none.fl_str_mv Ferrari, Fausto
Lederman, Claudia Beatriz
author Ferrari, Fausto
author_facet Ferrari, Fausto
Lederman, Claudia Beatriz
author_role author
author2 Lederman, Claudia Beatriz
author2_role author
dc.subject.none.fl_str_mv FREE BOUNDARY PROBLEM
SINGULAR / DEGENERATE OPERATOR
REGULARITY
VISCOSITY SOLUTIONS
topic FREE BOUNDARY PROBLEM
SINGULAR / DEGENERATE OPERATOR
REGULARITY
VISCOSITY SOLUTIONS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We consider viscosity solutions to two-phase free boundary problems for the p(x)-Laplacian with non-zero right hand side. We prove that flat free boundaries are C1,γ . No assumption on the Lipschitz continuity of solutions is made. These regularity results are the first ones in literature for two-phase free boundary problems for the p(x)-Laplacian and also for twophase problems for singular/degenerate operators with non-zero right hand side. They are new even when p(x) ≡ p, i.e., for the p-Laplacian. The fact that our results hold for merely viscosity solutions allows a wide applicability.
Fil: Ferrari, Fausto. Universidad de Bologna; Italia
Fil: Lederman, Claudia Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
description We consider viscosity solutions to two-phase free boundary problems for the p(x)-Laplacian with non-zero right hand side. We prove that flat free boundaries are C1,γ . No assumption on the Lipschitz continuity of solutions is made. These regularity results are the first ones in literature for two-phase free boundary problems for the p(x)-Laplacian and also for twophase problems for singular/degenerate operators with non-zero right hand side. They are new even when p(x) ≡ p, i.e., for the p-Laplacian. The fact that our results hold for merely viscosity solutions allows a wide applicability.
publishDate 2024
dc.date.none.fl_str_mv 2024-05
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/265089
Ferrari, Fausto; Lederman, Claudia Beatriz; Regularity of flat free boundaries for two-phase p(x)-Laplacian problems with right hand side; Springer; Calculus Of Variations And Partial Differential Equations; 63; 5; 5-2024; 1-43
0944-2669
1432-0835
CONICET Digital
CONICET
url http://hdl.handle.net/11336/265089
identifier_str_mv Ferrari, Fausto; Lederman, Claudia Beatriz; Regularity of flat free boundaries for two-phase p(x)-Laplacian problems with right hand side; Springer; Calculus Of Variations And Partial Differential Equations; 63; 5; 5-2024; 1-43
0944-2669
1432-0835
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/10.1007/s00526-024-02741-5
info:eu-repo/semantics/altIdentifier/doi/10.1007/s00526-024-02741-5
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 12.982451

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