Boundary value problems in graph Lipschitz domains in the plane with A∞-measures on the boundary

We prove several results for the Dirichlet, Neumann and Regularity problems for the Laplace equation in graph Lipschitz domains in the plane, considering A∞-measures on the boundary. More specifically, we study the Lp,1-solvability for the Dirichlet problem, complementing results of [25] and [10]. T...

Descripción completa

Detalles Bibliográficos
Autores: Ballesta Yagüe, Fernando, Carro Rossell, María Jesús
Tipo de recurso: artículo
Fecha de publicación:2026
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/130362
Acceso en línea:https://hdl.handle.net/20.500.14352/130362
Access Level:acceso abierto
Palabra clave:Dirichlet problem
Neumann problem
Regularity problem
Lipschitz graph domain
Lebesgue spaces
Muckenhoupt weights
Matemáticas (Matemáticas)
Ecuaciones diferenciales
12 Matemáticas
id ES_e64afcd6d6d005a389b3fd9d6d448caf
oai_identifier_str oai:docta.ucm.es:20.500.14352/130362
network_acronym_str ES
network_name_str España
repository_id_str
spelling Boundary value problems in graph Lipschitz domains in the plane with A∞-measures on the boundaryBallesta Yagüe, FernandoCarro Rossell, María JesúsDirichlet problemNeumann problemRegularity problemLipschitz graph domainLebesgue spacesMuckenhoupt weightsMatemáticas (Matemáticas)Ecuaciones diferenciales12 MatemáticasWe prove several results for the Dirichlet, Neumann and Regularity problems for the Laplace equation in graph Lipschitz domains in the plane, considering A∞-measures on the boundary. More specifically, we study the Lp,1-solvability for the Dirichlet problem, complementing results of [25] and [10]. Then, we study Lp-solvability of the Neumann problem, obtaining a range of solvability which is empty in some cases, a clear difference with the arc-length case. When it is not empty, it is an interval, and we consider solvability at its endpoints, establishing conditions for Lorentz space solvability when p>1and atomic Hardy space solvability when p =1. Solving the Lorentz endpoint leads us to a two-weight Sawyer-type inequality, for which we give a sufficient condition. Finally, we show how to adapt to the Regularity problem the results for the Neumann problem.ElsevierUniversidad Complutense de Madrid20262026-01-0120262026-01-01journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/130362reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)InglésengAgencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2020-113048GB-I00 ESPACIOS DE FUNCIONES Y TECNICAS DE ACOTACION DE OPERADORES EN ANALISISopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/1303622026-06-02T12:44:21Z
dc.title.none.fl_str_mv Boundary value problems in graph Lipschitz domains in the plane with A∞-measures on the boundary
title Boundary value problems in graph Lipschitz domains in the plane with A∞-measures on the boundary
spellingShingle Boundary value problems in graph Lipschitz domains in the plane with A∞-measures on the boundary
Ballesta Yagüe, Fernando
Dirichlet problem
Neumann problem
Regularity problem
Lipschitz graph domain
Lebesgue spaces
Muckenhoupt weights
Matemáticas (Matemáticas)
Ecuaciones diferenciales
12 Matemáticas
title_short Boundary value problems in graph Lipschitz domains in the plane with A∞-measures on the boundary
title_full Boundary value problems in graph Lipschitz domains in the plane with A∞-measures on the boundary
title_fullStr Boundary value problems in graph Lipschitz domains in the plane with A∞-measures on the boundary
title_full_unstemmed Boundary value problems in graph Lipschitz domains in the plane with A∞-measures on the boundary
title_sort Boundary value problems in graph Lipschitz domains in the plane with A∞-measures on the boundary
dc.creator.none.fl_str_mv Ballesta Yagüe, Fernando
Carro Rossell, María Jesús
author Ballesta Yagüe, Fernando
author_facet Ballesta Yagüe, Fernando
Carro Rossell, María Jesús
author_role author
author2 Carro Rossell, María Jesús
author2_role author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv Dirichlet problem
Neumann problem
Regularity problem
Lipschitz graph domain
Lebesgue spaces
Muckenhoupt weights
Matemáticas (Matemáticas)
Ecuaciones diferenciales
12 Matemáticas
topic Dirichlet problem
Neumann problem
Regularity problem
Lipschitz graph domain
Lebesgue spaces
Muckenhoupt weights
Matemáticas (Matemáticas)
Ecuaciones diferenciales
12 Matemáticas
description We prove several results for the Dirichlet, Neumann and Regularity problems for the Laplace equation in graph Lipschitz domains in the plane, considering A∞-measures on the boundary. More specifically, we study the Lp,1-solvability for the Dirichlet problem, complementing results of [25] and [10]. Then, we study Lp-solvability of the Neumann problem, obtaining a range of solvability which is empty in some cases, a clear difference with the arc-length case. When it is not empty, it is an interval, and we consider solvability at its endpoints, establishing conditions for Lorentz space solvability when p>1and atomic Hardy space solvability when p =1. Solving the Lorentz endpoint leads us to a two-weight Sawyer-type inequality, for which we give a sufficient condition. Finally, we show how to adapt to the Regularity problem the results for the Neumann problem.
publishDate 2026
dc.date.none.fl_str_mv 2026
2026-01-01
2026
2026-01-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14352/130362
url https://hdl.handle.net/20.500.14352/130362
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2020-113048GB-I00 ESPACIOS DE FUNCIONES Y TECNICAS DE ACOTACION DE OPERADORES EN ANALISIS
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://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
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Docta Complutense
instname:Universidad Complutense de Madrid (UCM)
instname_str Universidad Complutense de Madrid (UCM)
reponame_str Docta Complutense
collection Docta Complutense
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869422753822539776
score 15,812429

Similares en LA Referencia