A nonlocal 1-Laplacian problem and median values

Autores
Mazón, José M.; Pérez Pérez, Maria Teresa; Rossi, Julio Daniel; Toledo, Julián
Año de publicación
2016
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper, we study solutions to a nonlocal 1-Laplacian equation given by − Z ΩJ J(x − y) uψ(y) − u(x) |uψ(y) − u(x)| dy = 0 for x ∈ Ω with u(x) = ψ(x) for x ∈ ΩJ \ Ω. We introduce two notions of solution and prove that the weaker of the two concepts is equivalent to a nonlocal median value property, where the median is determined by a measure related to J. We also show that solutions in the stronger sense are nonlocal analogues of local least gradient functions, in the sense that they minimize a nonlocal functional. In addition, we prove that solutions in the stronger sense converge to least gradient solutions when the kernel J is appropriately rescaled.
Fil: Mazón, José M.. Universidad de Valencia; España
Fil: Pérez Pérez, Maria Teresa. Universidad Autónoma de Madrid; España. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Rossi, Julio Daniel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Toledo, Julián. Universidad de Valencia; España
Materia
1-laplacian
Mean value
Least gradient functions
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/19454
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/19454
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling A nonlocal 1-Laplacian problem and median valuesMazón, José M.Pérez Pérez, Maria TeresaRossi, Julio DanielToledo, Julián1-laplacianMean valueLeast gradient functionshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper, we study solutions to a nonlocal 1-Laplacian equation given by − Z ΩJ J(x − y) uψ(y) − u(x) |uψ(y) − u(x)| dy = 0 for x ∈ Ω with u(x) = ψ(x) for x ∈ ΩJ \ Ω. We introduce two notions of solution and prove that the weaker of the two concepts is equivalent to a nonlocal median value property, where the median is determined by a measure related to J. We also show that solutions in the stronger sense are nonlocal analogues of local least gradient functions, in the sense that they minimize a nonlocal functional. In addition, we prove that solutions in the stronger sense converge to least gradient solutions when the kernel J is appropriately rescaled.Fil: Mazón, José M.. Universidad de Valencia; EspañaFil: Pérez Pérez, Maria Teresa. Universidad Autónoma de Madrid; España. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Rossi, Julio Daniel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Toledo, Julián. Universidad de Valencia; EspañaUniversitat Autònoma de Barcelona2016info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/19454Mazón, José M.; Pérez Pérez, Maria Teresa; Rossi, Julio Daniel; Toledo, Julián; A nonlocal 1-Laplacian problem and median values; Universitat Autònoma de Barcelona; Publicacions Matematiques; 60; 1; -1-2016; 27-530214-14932014-4350CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.5565/PUBLMAT_60116_02info:eu-repo/semantics/altIdentifier/url/http://mat.uab.cat/pubmat/articles/view_doi/10.5565/PUBLMAT_60116_02info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-05T09:36:36Zoai:ri.conicet.gov.ar:11336/19454instacron: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:34982025-11-05 09:36:37.283CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A nonlocal 1-Laplacian problem and median values
title A nonlocal 1-Laplacian problem and median values
spellingShingle A nonlocal 1-Laplacian problem and median values
Mazón, José M.
1-laplacian
Mean value
Least gradient functions
title_short A nonlocal 1-Laplacian problem and median values
title_full A nonlocal 1-Laplacian problem and median values
title_fullStr A nonlocal 1-Laplacian problem and median values
title_full_unstemmed A nonlocal 1-Laplacian problem and median values
title_sort A nonlocal 1-Laplacian problem and median values
dc.creator.none.fl_str_mv Mazón, José M.
Pérez Pérez, Maria Teresa
Rossi, Julio Daniel
Toledo, Julián
author Mazón, José M.
author_facet Mazón, José M.
Pérez Pérez, Maria Teresa
Rossi, Julio Daniel
Toledo, Julián
author_role author
author2 Pérez Pérez, Maria Teresa
Rossi, Julio Daniel
Toledo, Julián
author2_role author
author
author
dc.subject.none.fl_str_mv 1-laplacian
Mean value
Least gradient functions
topic 1-laplacian
Mean value
Least gradient functions
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this paper, we study solutions to a nonlocal 1-Laplacian equation given by − Z ΩJ J(x − y) uψ(y) − u(x) |uψ(y) − u(x)| dy = 0 for x ∈ Ω with u(x) = ψ(x) for x ∈ ΩJ \ Ω. We introduce two notions of solution and prove that the weaker of the two concepts is equivalent to a nonlocal median value property, where the median is determined by a measure related to J. We also show that solutions in the stronger sense are nonlocal analogues of local least gradient functions, in the sense that they minimize a nonlocal functional. In addition, we prove that solutions in the stronger sense converge to least gradient solutions when the kernel J is appropriately rescaled.
Fil: Mazón, José M.. Universidad de Valencia; España
Fil: Pérez Pérez, Maria Teresa. Universidad Autónoma de Madrid; España. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Rossi, Julio Daniel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Toledo, Julián. Universidad de Valencia; España
description In this paper, we study solutions to a nonlocal 1-Laplacian equation given by − Z ΩJ J(x − y) uψ(y) − u(x) |uψ(y) − u(x)| dy = 0 for x ∈ Ω with u(x) = ψ(x) for x ∈ ΩJ \ Ω. We introduce two notions of solution and prove that the weaker of the two concepts is equivalent to a nonlocal median value property, where the median is determined by a measure related to J. We also show that solutions in the stronger sense are nonlocal analogues of local least gradient functions, in the sense that they minimize a nonlocal functional. In addition, we prove that solutions in the stronger sense converge to least gradient solutions when the kernel J is appropriately rescaled.
publishDate 2016
dc.date.none.fl_str_mv 2016
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/11336/19454
Mazón, José M.; Pérez Pérez, Maria Teresa; Rossi, Julio Daniel; Toledo, Julián; A nonlocal 1-Laplacian problem and median values; Universitat Autònoma de Barcelona; Publicacions Matematiques; 60; 1; -1-2016; 27-53
0214-1493
2014-4350
CONICET Digital
CONICET
url http://hdl.handle.net/11336/19454
identifier_str_mv Mazón, José M.; Pérez Pérez, Maria Teresa; Rossi, Julio Daniel; Toledo, Julián; A nonlocal 1-Laplacian problem and median values; Universitat Autònoma de Barcelona; Publicacions Matematiques; 60; 1; -1-2016; 27-53
0214-1493
2014-4350
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.5565/PUBLMAT_60116_02
info:eu-repo/semantics/altIdentifier/url/http://mat.uab.cat/pubmat/articles/view_doi/10.5565/PUBLMAT_60116_02
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Universitat Autònoma de Barcelona
publisher.none.fl_str_mv Universitat Autònoma de Barcelona
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 13.082534

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