An explicit right inverse of the divergence operator which is continuous in weighted norms : Notas de Matemática, 72

The existence of a continuous right inverse of the divergence operator in W01'p(Ω)n, 1 < p < ∞, is a well known result which is basic in the analysis of the Stokes equations. The object of this paper is to give a constructive proof of the existence of such an operator and to show...

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Autores principales: Durán, Ricardo Guillermo, Muschietti, María Amelia
Formato: Publicacion seriada
Lenguaje:Inglés
Publicado: 2000
Materias:
Matemática
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/172777
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SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-172777
record_format dspace
spelling I19-R120-10915-1727772024-11-08T04:10:43Z http://sedici.unlp.edu.ar/handle/10915/172777 An explicit right inverse of the divergence operator which is continuous in weighted norms : Notas de Matemática, 72 Durán, Ricardo Guillermo Muschietti, María Amelia 2000 2024-11-07T16:12:03Z en Matemática The existence of a continuous right inverse of the divergence operator in W01'p(Ω)n, 1 < p < ∞, is a well known result which is basic in the analysis of the Stokes equations. The object of this paper is to give a constructive proof of the existence of such an operator and to show that the continuity holds also for some weighted norms. Our results are valid for Ω C IP.π a bounded domain which is star-shaped with respect to a ball B C Ω. The continuity results are obtained by using the classical theory of singular integrals of Calderon and Zygmund and 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 to extend to the three dimensional case the general results on uniform convergence of finite element approximations of the Stokes equations. Material digitalizado en SEDICI gracias a la colaboración de la Biblioteca del Departamento de Matemática de la Facultad de Ciencias Exactas (UNLP). Facultad de Ciencias Exactas Publicacion seriada Publicacion seriada http://creativecommons.org/licenses/by-nc-sa/4.0/ Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) application/pdf
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Matemática
spellingShingle Matemática
Durán, Ricardo Guillermo
Muschietti, María Amelia
An explicit right inverse of the divergence operator which is continuous in weighted norms : Notas de Matemática, 72
topic_facet Matemática
description The existence of a continuous right inverse of the divergence operator in W01'p(Ω)n, 1 < p < ∞, is a well known result which is basic in the analysis of the Stokes equations. The object of this paper is to give a constructive proof of the existence of such an operator and to show that the continuity holds also for some weighted norms. Our results are valid for Ω C IP.π a bounded domain which is star-shaped with respect to a ball B C Ω. The continuity results are obtained by using the classical theory of singular integrals of Calderon and Zygmund and 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 to extend to the three dimensional case the general results on uniform convergence of finite element approximations of the Stokes equations.
format Publicacion seriada
Publicacion seriada
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 : Notas de Matemática, 72
title_short An explicit right inverse of the divergence operator which is continuous in weighted norms : Notas de Matemática, 72
title_full An explicit right inverse of the divergence operator which is continuous in weighted norms : Notas de Matemática, 72
title_fullStr An explicit right inverse of the divergence operator which is continuous in weighted norms : Notas de Matemática, 72
title_full_unstemmed An explicit right inverse of the divergence operator which is continuous in weighted norms : Notas de Matemática, 72
title_sort explicit right inverse of the divergence operator which is continuous in weighted norms : notas de matemática, 72
publishDate 2000
url http://sedici.unlp.edu.ar/handle/10915/172777
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