An asymptotic mean value characterization for p-harmonic functions

Autores
Manfredi, Juan J.; Parviainen, Mikko; Rossi, Julio Daniel
Año de publicación
2010
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We characterize p-harmonic functions in terms of an asymptotic mean value property. A p-harmonic function u is a viscosity solution to ∆pu = div(|∇u| p−2∇u) = 0 with 1 < p ≤ ∞ in a domain Ω if and only if the expansion u(x) = α 2 max Bε(x) u + min Bε(x) u + β |Bε(x)| Bε(x) u dy + o(ε2) holds as ε → 0 for x ∈ Ω in a weak sense, which we call the viscosity sense. Here the coefficients α, β are determined by α + β = 1 and α/β = (p − 2)/(N + 2).
Fil: Manfredi, Juan J.. No especifíca;
Fil: Parviainen, Mikko. No especifíca;
Fil: Rossi, Julio Daniel. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
Mean Value Properties
P-Laplacian
Infinity Laplacian
Viscosity Solutions
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:11336/16396
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/16396
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling An asymptotic mean value characterization for p-harmonic functionsManfredi, Juan J.Parviainen, MikkoRossi, Julio DanielMean Value PropertiesP-LaplacianInfinity LaplacianViscosity Solutionshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We characterize p-harmonic functions in terms of an asymptotic mean value property. A p-harmonic function u is a viscosity solution to ∆pu = div(|∇u| p−2∇u) = 0 with 1 < p ≤ ∞ in a domain Ω if and only if the expansion u(x) = α 2 max Bε(x) u + min Bε(x) u + β |Bε(x)| Bε(x) u dy + o(ε2) holds as ε → 0 for x ∈ Ω in a weak sense, which we call the viscosity sense. Here the coefficients α, β are determined by α + β = 1 and α/β = (p − 2)/(N + 2).Fil: Manfredi, Juan J.. No especifíca;Fil: Parviainen, Mikko. No especifíca;Fil: Rossi, Julio Daniel. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaAmerican Mathematical Society2010-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/16396Manfredi, Juan J.; Parviainen, Mikko; Rossi, Julio Daniel; An asymptotic mean value characterization for p-harmonic functions; American Mathematical Society; Proceedings Of The American Mathematical Society; 138; 3; 3-2010; 881-8890002-99391088-6826enginfo:eu-repo/semantics/altIdentifier/doi/10.1090/S0002-9939-09-10183-1info:eu-repo/semantics/altIdentifier/url/http://www.ams.org/journals/proc/2010-138-03/S0002-9939-09-10183-1/home.htmlinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:06:42Zoai:ri.conicet.gov.ar:11336/16396instacron: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:34982025-09-29 10:06:42.962CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv An asymptotic mean value characterization for p-harmonic functions
title An asymptotic mean value characterization for p-harmonic functions
spellingShingle An asymptotic mean value characterization for p-harmonic functions
Manfredi, Juan J.
Mean Value Properties
P-Laplacian
Infinity Laplacian
Viscosity Solutions
title_short An asymptotic mean value characterization for p-harmonic functions
title_full An asymptotic mean value characterization for p-harmonic functions
title_fullStr An asymptotic mean value characterization for p-harmonic functions
title_full_unstemmed An asymptotic mean value characterization for p-harmonic functions
title_sort An asymptotic mean value characterization for p-harmonic functions
dc.creator.none.fl_str_mv Manfredi, Juan J.
Parviainen, Mikko
Rossi, Julio Daniel
author Manfredi, Juan J.
author_facet Manfredi, Juan J.
Parviainen, Mikko
Rossi, Julio Daniel
author_role author
author2 Parviainen, Mikko
Rossi, Julio Daniel
author2_role author
author
dc.subject.none.fl_str_mv Mean Value Properties
P-Laplacian
Infinity Laplacian
Viscosity Solutions
topic Mean Value Properties
P-Laplacian
Infinity Laplacian
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 characterize p-harmonic functions in terms of an asymptotic mean value property. A p-harmonic function u is a viscosity solution to ∆pu = div(|∇u| p−2∇u) = 0 with 1 < p ≤ ∞ in a domain Ω if and only if the expansion u(x) = α 2 max Bε(x) u + min Bε(x) u + β |Bε(x)| Bε(x) u dy + o(ε2) holds as ε → 0 for x ∈ Ω in a weak sense, which we call the viscosity sense. Here the coefficients α, β are determined by α + β = 1 and α/β = (p − 2)/(N + 2).
Fil: Manfredi, Juan J.. No especifíca;
Fil: Parviainen, Mikko. No especifíca;
Fil: Rossi, Julio Daniel. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description We characterize p-harmonic functions in terms of an asymptotic mean value property. A p-harmonic function u is a viscosity solution to ∆pu = div(|∇u| p−2∇u) = 0 with 1 < p ≤ ∞ in a domain Ω if and only if the expansion u(x) = α 2 max Bε(x) u + min Bε(x) u + β |Bε(x)| Bε(x) u dy + o(ε2) holds as ε → 0 for x ∈ Ω in a weak sense, which we call the viscosity sense. Here the coefficients α, β are determined by α + β = 1 and α/β = (p − 2)/(N + 2).
publishDate 2010
dc.date.none.fl_str_mv 2010-03
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/11336/16396
Manfredi, Juan J.; Parviainen, Mikko; Rossi, Julio Daniel; An asymptotic mean value characterization for p-harmonic functions; American Mathematical Society; Proceedings Of The American Mathematical Society; 138; 3; 3-2010; 881-889
0002-9939
1088-6826
url http://hdl.handle.net/11336/16396
identifier_str_mv Manfredi, Juan J.; Parviainen, Mikko; Rossi, Julio Daniel; An asymptotic mean value characterization for p-harmonic functions; American Mathematical Society; Proceedings Of The American Mathematical Society; 138; 3; 3-2010; 881-889
0002-9939
1088-6826
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1090/S0002-9939-09-10183-1
info:eu-repo/semantics/altIdentifier/url/http://www.ams.org/journals/proc/2010-138-03/S0002-9939-09-10183-1/home.html
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 American Mathematical Society
publisher.none.fl_str_mv American Mathematical Society
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
_version_ 1844613919316901888
score 13.070432

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