Improved Poincaré inequalities with weights

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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...

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Autores principales: Drelichman, I., Durán, R.G.
Formato: Artículo publishedVersion
Lenguaje:Inglés
Publicado: 2008
Materias:
John domains
Reverse doubling weights
Weighted Poincaré inequality
Weighted Sobolev inequality
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_0022247X_v347_n1_p286_Drelichman
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paperaa:paper_0022247X_v347_n1_p286_Drelichman
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spelling paperaa:paper_0022247X_v347_n1_p286_Drelichman2023-06-12T16:44:09Z Improved Poincaré inequalities with weights J. Math. Anal. Appl. 2008;347(1):286-293 Drelichman, I. Durán, R.G. John domains Reverse doubling weights Weighted Poincaré inequality Weighted Sobolev inequality 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. 2008 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion application/pdf eng info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_0022247X_v347_n1_p286_Drelichman
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
language Inglés
orig_language_str_mv eng
topic John domains
Reverse doubling weights
Weighted Poincaré inequality
Weighted Sobolev inequality
spellingShingle John domains
Reverse doubling weights
Weighted Poincaré inequality
Weighted Sobolev inequality
Drelichman, I.
Durán, R.G.
Improved Poincaré inequalities with weights
topic_facet John domains
Reverse doubling weights
Weighted Poincaré inequality
Weighted Sobolev inequality
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.
format Artículo
Artículo
publishedVersion
author Drelichman, I.
Durán, R.G.
author_facet Drelichman, I.
Durán, R.G.
author_sort Drelichman, I.
title Improved Poincaré inequalities with weights
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
publishDate 2008
url http://hdl.handle.net/20.500.12110/paper_0022247X_v347_n1_p286_Drelichman
work_keys_str_mv AT drelichmani improvedpoincareinequalitieswithweights
AT duranrg improvedpoincareinequalitieswithweights
_version_ 1769810165902606336

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