Improved Poincaré inequalities with weights

Autores
Drelichman, I.; Durán, R.G.
Año de publicación
2008
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper we prove that if Ω ∈ Rn is a bounded John domain, the following weighted Poincaré-type inequality holds:under(inf, a ∈ R) {norm of matrix} f (x) - a {norm of matrix}Lq (Ω, w1) ≤ C {norm of matrix} ∇ f (x) d (x)α {norm of matrix}Lp (Ω, w2) where f is a locally Lipschitz function on Ω, d (x) denotes the distance of x to the boundary of Ω, the weights w1, w2 satisfy certain cube conditions, and α ∈ [0, 1] depends on p, q and n. This result generalizes previously known weighted inequalities, which can also be obtained with our approach. © 2008 Elsevier Inc. All rights reserved.
Fil:Drelichman, I. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Durán, R.G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fuente
J. Math. Anal. Appl. 2008;347(1):286-293
Materia
John domains
Reverse doubling weights
Weighted Poincaré inequality
Weighted Sobolev inequality
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by/2.5/ar
Repositorio
Biblioteca Digital (UBA-FCEN)
Institución
Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
OAI Identificador
paperaa:paper_0022247X_v347_n1_p286_Drelichman
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oai_identifier_str paperaa:paper_0022247X_v347_n1_p286_Drelichman
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repository_id_str 1896
network_name_str Biblioteca Digital (UBA-FCEN)
spelling Improved Poincaré inequalities with weightsDrelichman, I.Durán, R.G.John domainsReverse doubling weightsWeighted Poincaré inequalityWeighted Sobolev inequalityIn this paper we prove that if Ω ∈ Rn is a bounded John domain, the following weighted Poincaré-type inequality holds:under(inf, a ∈ R) {norm of matrix} f (x) - a {norm of matrix}Lq (Ω, w1) ≤ C {norm of matrix} ∇ f (x) d (x)α {norm of matrix}Lp (Ω, w2) where f is a locally Lipschitz function on Ω, d (x) denotes the distance of x to the boundary of Ω, the weights w1, w2 satisfy certain cube conditions, and α ∈ [0, 1] depends on p, q and n. This result generalizes previously known weighted inequalities, which can also be obtained with our approach. © 2008 Elsevier Inc. All rights reserved.Fil:Drelichman, I. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.Fil:Durán, R.G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.2008info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfhttp://hdl.handle.net/20.500.12110/paper_0022247X_v347_n1_p286_DrelichmanJ. Math. Anal. Appl. 2008;347(1):286-293reponame:Biblioteca Digital (UBA-FCEN)instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesinstacron:UBA-FCENenginfo:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/2.5/ar2025-11-06T09:39:43Zpaperaa:paper_0022247X_v347_n1_p286_DrelichmanInstitucionalhttps://digital.bl.fcen.uba.ar/Universidad públicaNo correspondehttps://digital.bl.fcen.uba.ar/cgi-bin/oaiserver.cgiana@bl.fcen.uba.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:18962025-11-06 09:39:45.06Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesfalse
dc.title.none.fl_str_mv Improved Poincaré inequalities with weights
title Improved Poincaré inequalities with weights
spellingShingle Improved Poincaré inequalities with weights
Drelichman, I.
John domains
Reverse doubling weights
Weighted Poincaré inequality
Weighted Sobolev inequality
title_short Improved Poincaré inequalities with weights
title_full Improved Poincaré inequalities with weights
title_fullStr Improved Poincaré inequalities with weights
title_full_unstemmed Improved Poincaré inequalities with weights
title_sort Improved Poincaré inequalities with weights
dc.creator.none.fl_str_mv Drelichman, I.
Durán, R.G.
author Drelichman, I.
author_facet Drelichman, I.
Durán, R.G.
author_role author
author2 Durán, R.G.
author2_role author
dc.subject.none.fl_str_mv John domains
Reverse doubling weights
Weighted Poincaré inequality
Weighted Sobolev inequality
topic John domains
Reverse doubling weights
Weighted Poincaré inequality
Weighted Sobolev inequality
dc.description.none.fl_txt_mv In this paper we prove that if Ω ∈ Rn is a bounded John domain, the following weighted Poincaré-type inequality holds:under(inf, a ∈ R) {norm of matrix} f (x) - a {norm of matrix}Lq (Ω, w1) ≤ C {norm of matrix} ∇ f (x) d (x)α {norm of matrix}Lp (Ω, w2) where f is a locally Lipschitz function on Ω, d (x) denotes the distance of x to the boundary of Ω, the weights w1, w2 satisfy certain cube conditions, and α ∈ [0, 1] depends on p, q and n. This result generalizes previously known weighted inequalities, which can also be obtained with our approach. © 2008 Elsevier Inc. All rights reserved.
Fil:Drelichman, I. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Durán, R.G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
description In this paper we prove that if Ω ∈ Rn is a bounded John domain, the following weighted Poincaré-type inequality holds:under(inf, a ∈ R) {norm of matrix} f (x) - a {norm of matrix}Lq (Ω, w1) ≤ C {norm of matrix} ∇ f (x) d (x)α {norm of matrix}Lp (Ω, w2) where f is a locally Lipschitz function on Ω, d (x) denotes the distance of x to the boundary of Ω, the weights w1, w2 satisfy certain cube conditions, and α ∈ [0, 1] depends on p, q and n. This result generalizes previously known weighted inequalities, which can also be obtained with our approach. © 2008 Elsevier Inc. All rights reserved.
publishDate 2008
dc.date.none.fl_str_mv 2008
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/20.500.12110/paper_0022247X_v347_n1_p286_Drelichman
url http://hdl.handle.net/20.500.12110/paper_0022247X_v347_n1_p286_Drelichman
dc.language.none.fl_str_mv eng
language eng
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/2.5/ar
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by/2.5/ar
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv J. Math. Anal. Appl. 2008;347(1):286-293
reponame:Biblioteca Digital (UBA-FCEN)
instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron:UBA-FCEN
reponame_str Biblioteca Digital (UBA-FCEN)
collection Biblioteca Digital (UBA-FCEN)
instname_str Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron_str UBA-FCEN
institution UBA-FCEN
repository.name.fl_str_mv Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
repository.mail.fl_str_mv ana@bl.fcen.uba.ar
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score 12.976206

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