An explicit right inverse of the divergence operator which is continuous in weighted norms

The existence of a continuous right inverse of the divergence operator in W<SUP>1,p</SUP><SUB>0</SUB> (Ω)<SUP>n</SUP>, 1 < p < ∞, is a well known result which is basic in the analysis of the Stokes equations. The object of this paper is to show that the cont...

Descripción completa

Detalles Bibliográficos
Autores principales: Durán, Ricardo Guillermo, Muschietti, María Amelia
Formato: Articulo
Lenguaje:Inglés
Publicado: 2001
Materias:
Ciencias Exactas
Divergence operator
Finite elements
Singular integrals
Stokes equations
Weighted estimates
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/83495
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-83495
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Ciencias Exactas
Divergence operator
Finite elements
Singular integrals
Stokes equations
Weighted estimates
spellingShingle Ciencias Exactas
Divergence operator
Finite elements
Singular integrals
Stokes equations
Weighted estimates
Durán, Ricardo Guillermo
Muschietti, María Amelia
An explicit right inverse of the divergence operator which is continuous in weighted norms
topic_facet Ciencias Exactas
Divergence operator
Finite elements
Singular integrals
Stokes equations
Weighted estimates
description The existence of a continuous right inverse of the divergence operator in W<SUP>1,p</SUP><SUB>0</SUB> (Ω)<SUP>n</SUP>, 1 < p < ∞, is a well known result which is basic in the analysis of the Stokes equations. The object of this paper is to show that the continuity also holds for some weighted norms. Our results are valid for Ω ⊂ ℝ<SUP>n</SUP> a bounded domain which is star-shaped with respect to a ball B ⊂ Ω. The continuity results are obtained by using an explicit solution of the divergence equation and the classical theory of singular integrals of Calderón and Zygmund together with general results on weighted estimates proven by Stein. The weights considered here are of interest in the analysis of finite element methods. In particular, our result allows us to extend to the three-dimensional case the general results on uniform convergence of finite element approximations of the Stokes equations.
format Articulo
Articulo
author Durán, Ricardo Guillermo
Muschietti, María Amelia
author_facet Durán, Ricardo Guillermo
Muschietti, María Amelia
author_sort Durán, Ricardo Guillermo
title An explicit right inverse of the divergence operator which is continuous in weighted norms
title_short An explicit right inverse of the divergence operator which is continuous in weighted norms
title_full An explicit right inverse of the divergence operator which is continuous in weighted norms
title_fullStr An explicit right inverse of the divergence operator which is continuous in weighted norms
title_full_unstemmed An explicit right inverse of the divergence operator which is continuous in weighted norms
title_sort explicit right inverse of the divergence operator which is continuous in weighted norms
publishDate 2001
url http://sedici.unlp.edu.ar/handle/10915/83495
work_keys_str_mv AT duranricardoguillermo anexplicitrightinverseofthedivergenceoperatorwhichiscontinuousinweightednorms
AT muschiettimariaamelia anexplicitrightinverseofthedivergenceoperatorwhichiscontinuousinweightednorms
AT duranricardoguillermo explicitrightinverseofthedivergenceoperatorwhichiscontinuousinweightednorms
AT muschiettimariaamelia explicitrightinverseofthedivergenceoperatorwhichiscontinuousinweightednorms
bdutipo_str Repositorios
_version_ 1764820488671985668

Ejemplares similares