Improvement of Besov regularity for solutions of the fractional Laplacian

Autores
Aimar, Hugo Alejandro; Beltritti, Gastón; Gomez, Ivana Daniela
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We prove a mean value formula for weak solutions of div(|y| agradu) = 0 in Rn+1 = {(x, y) : x ∈ Rn, y ∈ R}, −1 < a < 1, and balls centered at points of the form (x, 0). We obtain an explicit nonlocal kernel for the mean value formula for solutions of (−)s f = 0 on a domain D of Rn. When D is Lipschitz, we prove a Besov type regularity improvement for the solutions of (−)s f = 0.
Fil: Aimar, Hugo Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Matemática Aplicada "Litoral"; Argentina
Fil: Beltritti, Gastón. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Matemática Aplicada "Litoral"; Argentina
Fil: Gomez, Ivana Daniela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Matemática Aplicada "Litoral"; Argentina
Materia
Degenerate Elliptic Equations
Fractional Laplacian
Mean Value Formula
Besov Spaces
Gradient Estimates
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:11336/9379
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/9379
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Improvement of Besov regularity for solutions of the fractional LaplacianAimar, Hugo AlejandroBeltritti, GastónGomez, Ivana DanielaDegenerate Elliptic EquationsFractional LaplacianMean Value FormulaBesov SpacesGradient Estimateshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We prove a mean value formula for weak solutions of div(|y| agradu) = 0 in Rn+1 = {(x, y) : x ∈ Rn, y ∈ R}, −1 < a < 1, and balls centered at points of the form (x, 0). We obtain an explicit nonlocal kernel for the mean value formula for solutions of (−)s f = 0 on a domain D of Rn. When D is Lipschitz, we prove a Besov type regularity improvement for the solutions of (−)s f = 0.Fil: Aimar, Hugo Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Matemática Aplicada "Litoral"; ArgentinaFil: Beltritti, Gastón. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Matemática Aplicada "Litoral"; ArgentinaFil: Gomez, Ivana Daniela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Matemática Aplicada "Litoral"; ArgentinaSpringer2014-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/9379Aimar, Hugo Alejandro; Beltritti, Gastón; Gomez, Ivana Daniela; Improvement of Besov regularity for solutions of the fractional Laplacian; Springer; Constructive Approximation; 41; 2; 8-2014; 219-2290176-4276enginfo:eu-repo/semantics/altIdentifier/doi//10.1007/s00365-014-9256-0info:eu-repo/semantics/altIdentifier/url/http://link.springer.com/article/10.1007%2Fs00365-014-9256-0info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-05T09:56:19Zoai:ri.conicet.gov.ar:11336/9379instacron: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 09:56:20.13CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Improvement of Besov regularity for solutions of the fractional Laplacian
title Improvement of Besov regularity for solutions of the fractional Laplacian
spellingShingle Improvement of Besov regularity for solutions of the fractional Laplacian
Aimar, Hugo Alejandro
Degenerate Elliptic Equations
Fractional Laplacian
Mean Value Formula
Besov Spaces
Gradient Estimates
title_short Improvement of Besov regularity for solutions of the fractional Laplacian
title_full Improvement of Besov regularity for solutions of the fractional Laplacian
title_fullStr Improvement of Besov regularity for solutions of the fractional Laplacian
title_full_unstemmed Improvement of Besov regularity for solutions of the fractional Laplacian
title_sort Improvement of Besov regularity for solutions of the fractional Laplacian
dc.creator.none.fl_str_mv Aimar, Hugo Alejandro
Beltritti, Gastón
Gomez, Ivana Daniela
author Aimar, Hugo Alejandro
author_facet Aimar, Hugo Alejandro
Beltritti, Gastón
Gomez, Ivana Daniela
author_role author
author2 Beltritti, Gastón
Gomez, Ivana Daniela
author2_role author
author
dc.subject.none.fl_str_mv Degenerate Elliptic Equations
Fractional Laplacian
Mean Value Formula
Besov Spaces
Gradient Estimates
topic Degenerate Elliptic Equations
Fractional Laplacian
Mean Value Formula
Besov Spaces
Gradient Estimates
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 prove a mean value formula for weak solutions of div(|y| agradu) = 0 in Rn+1 = {(x, y) : x ∈ Rn, y ∈ R}, −1 < a < 1, and balls centered at points of the form (x, 0). We obtain an explicit nonlocal kernel for the mean value formula for solutions of (−)s f = 0 on a domain D of Rn. When D is Lipschitz, we prove a Besov type regularity improvement for the solutions of (−)s f = 0.
Fil: Aimar, Hugo Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Matemática Aplicada "Litoral"; Argentina
Fil: Beltritti, Gastón. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Matemática Aplicada "Litoral"; Argentina
Fil: Gomez, Ivana Daniela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Matemática Aplicada "Litoral"; Argentina
description We prove a mean value formula for weak solutions of div(|y| agradu) = 0 in Rn+1 = {(x, y) : x ∈ Rn, y ∈ R}, −1 < a < 1, and balls centered at points of the form (x, 0). We obtain an explicit nonlocal kernel for the mean value formula for solutions of (−)s f = 0 on a domain D of Rn. When D is Lipschitz, we prove a Besov type regularity improvement for the solutions of (−)s f = 0.
publishDate 2014
dc.date.none.fl_str_mv 2014-08
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/11336/9379
Aimar, Hugo Alejandro; Beltritti, Gastón; Gomez, Ivana Daniela; Improvement of Besov regularity for solutions of the fractional Laplacian; Springer; Constructive Approximation; 41; 2; 8-2014; 219-229
0176-4276
url http://hdl.handle.net/11336/9379
identifier_str_mv Aimar, Hugo Alejandro; Beltritti, Gastón; Gomez, Ivana Daniela; Improvement of Besov regularity for solutions of the fractional Laplacian; Springer; Constructive Approximation; 41; 2; 8-2014; 219-229
0176-4276
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi//10.1007/s00365-014-9256-0
info:eu-repo/semantics/altIdentifier/url/http://link.springer.com/article/10.1007%2Fs00365-014-9256-0
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
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 13.082534

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