Improved Poincaré inequalities and solutions of the divergence in weighted norms

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The improved Poincaré inequality ∣∣φ-φΩ∣∣ Lp(Ω)≤C ∣∣d∇φ Lp(Ω) Where Ω ⊂ Rn is a bounded domain and d(x) is the distance from x to the boundary of Ω, has many applications. In particular, it can be used to obtain a decomposition of functions with vanishing integral into a sum of locally supported fu...

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Detalles Bibliográficos
Autores principales: Acosta, Gabriel, Cejas, María Eugenia, Durán, Ricardo Guillermo
Formato: Articulo
Lenguaje:Inglés
Publicado: 2017
Materias:
Matemática
Divergence operator
Poincaré inequalities
Weights
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/87652
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-87652
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Matemática
Divergence operator
Poincaré inequalities
Weights
spellingShingle Matemática
Divergence operator
Poincaré inequalities
Weights
Acosta, Gabriel
Cejas, María Eugenia
Durán, Ricardo Guillermo
Improved Poincaré inequalities and solutions of the divergence in weighted norms
topic_facet Matemática
Divergence operator
Poincaré inequalities
Weights
description The improved Poincaré inequality ∣∣φ-φΩ∣∣ Lp(Ω)≤C ∣∣d∇φ Lp(Ω) Where Ω ⊂ Rn is a bounded domain and d(x) is the distance from x to the boundary of Ω, has many applications. In particular, it can be used to obtain a decomposition of functions with vanishing integral into a sum of locally supported functions with the same property. Consequently, it can be used to go from local to global results, i.e., to extend to very general bounded domains results which are known for cubes. For example, this methodology can be used to prove the existence of solutions of the divergence in Sobolev spaces. The goal of this paper is to analyze the generalization of these results to the case of weighted norms. When the weight is in Ap the arguments used in the un-weighted case can be extended without great difficulty. However, we will show that the improved Poincaré inequality, as well as its above mentioned applications, can be extended to a more general class of weights.
format Articulo
Articulo
author Acosta, Gabriel
Cejas, María Eugenia
Durán, Ricardo Guillermo
author_facet Acosta, Gabriel
Cejas, María Eugenia
Durán, Ricardo Guillermo
author_sort Acosta, Gabriel
title Improved Poincaré inequalities and solutions of the divergence in weighted norms
title_short Improved Poincaré inequalities and solutions of the divergence in weighted norms
title_full Improved Poincaré inequalities and solutions of the divergence in weighted norms
title_fullStr Improved Poincaré inequalities and solutions of the divergence in weighted norms
title_full_unstemmed Improved Poincaré inequalities and solutions of the divergence in weighted norms
title_sort improved poincaré inequalities and solutions of the divergence in weighted norms
publishDate 2017
url http://sedici.unlp.edu.ar/handle/10915/87652
work_keys_str_mv AT acostagabriel improvedpoincareinequalitiesandsolutionsofthedivergenceinweightednorms
AT cejasmariaeugenia improvedpoincareinequalitiesandsolutionsofthedivergenceinweightednorms
AT duranricardoguillermo improvedpoincareinequalitiesandsolutionsofthedivergenceinweightednorms
bdutipo_str Repositorios
_version_ 1764820489254993922

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