Weighted Poincaré and Korn inequalities for Hölder α domains

It is known that the classic Korn inequality is not valid for Hölder α domains. In this paper, we prove a family of weaker inequalities for this kind of domains, replacing the standard Lp-norms by weighted norms where the weights are powers of the distance to the boundary. In order to obtain these r...

Descripción completa

Guardado en:
Detalles Bibliográficos
Autores principales: Acosta Rodriguez, Gabriel, Duran, Ricardo Guillermo, Lombardi, Ariel L.
Publicado: 2006
Materias:
Inequalities
Korn inequality
Non-smooth domains
Poincaré
Boundary conditions
Distance measurement
Standards
Numerical methods
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01704214_v29_n4_p387_Acosta
http://hdl.handle.net/20.500.12110/paper_01704214_v29_n4_p387_Acosta
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_01704214_v29_n4_p387_Acosta
record_format dspace
spelling paper:paper_01704214_v29_n4_p387_Acosta2023-06-08T15:18:36Z Weighted Poincaré and Korn inequalities for Hölder α domains Acosta Rodriguez, Gabriel Duran, Ricardo Guillermo Lombardi, Ariel L. Inequalities Korn inequality Non-smooth domains Poincaré Boundary conditions Distance measurement Standards Inequalities Korn inequality Non-smooth domains Poincaré Numerical methods It is known that the classic Korn inequality is not valid for Hölder α domains. In this paper, we prove a family of weaker inequalities for this kind of domains, replacing the standard Lp-norms by weighted norms where the weights are powers of the distance to the boundary. In order to obtain these results we prove first some weighted Poincaré inequalities and then, generalizing an argument of Kondratiev and Oleinik, we show that weighted Korn inequalities can be derived from them. The Poincaré type inequalities proved here improve previously known results. We show by means of examples that our results are optimal. Copyright © 2005 John Wiley & Sons, Ltd. Fil:Acosta, G. 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. Fil:Lombardi, A.L. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2006 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01704214_v29_n4_p387_Acosta http://hdl.handle.net/20.500.12110/paper_01704214_v29_n4_p387_Acosta
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Inequalities
Korn inequality
Non-smooth domains
Poincaré
Boundary conditions
Distance measurement
Standards
Inequalities
Korn inequality
Non-smooth domains
Poincaré
Numerical methods
spellingShingle Inequalities
Korn inequality
Non-smooth domains
Poincaré
Boundary conditions
Distance measurement
Standards
Inequalities
Korn inequality
Non-smooth domains
Poincaré
Numerical methods
Acosta Rodriguez, Gabriel
Duran, Ricardo Guillermo
Lombardi, Ariel L.
Weighted Poincaré and Korn inequalities for Hölder α domains
topic_facet Inequalities
Korn inequality
Non-smooth domains
Poincaré
Boundary conditions
Distance measurement
Standards
Inequalities
Korn inequality
Non-smooth domains
Poincaré
Numerical methods
description It is known that the classic Korn inequality is not valid for Hölder α domains. In this paper, we prove a family of weaker inequalities for this kind of domains, replacing the standard Lp-norms by weighted norms where the weights are powers of the distance to the boundary. In order to obtain these results we prove first some weighted Poincaré inequalities and then, generalizing an argument of Kondratiev and Oleinik, we show that weighted Korn inequalities can be derived from them. The Poincaré type inequalities proved here improve previously known results. We show by means of examples that our results are optimal. Copyright © 2005 John Wiley & Sons, Ltd.
author Acosta Rodriguez, Gabriel
Duran, Ricardo Guillermo
Lombardi, Ariel L.
author_facet Acosta Rodriguez, Gabriel
Duran, Ricardo Guillermo
Lombardi, Ariel L.
author_sort Acosta Rodriguez, Gabriel
title Weighted Poincaré and Korn inequalities for Hölder α domains
title_short Weighted Poincaré and Korn inequalities for Hölder α domains
title_full Weighted Poincaré and Korn inequalities for Hölder α domains
title_fullStr Weighted Poincaré and Korn inequalities for Hölder α domains
title_full_unstemmed Weighted Poincaré and Korn inequalities for Hölder α domains
title_sort weighted poincaré and korn inequalities for hölder α domains
publishDate 2006
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01704214_v29_n4_p387_Acosta
http://hdl.handle.net/20.500.12110/paper_01704214_v29_n4_p387_Acosta
work_keys_str_mv AT acostarodriguezgabriel weightedpoincareandkorninequalitiesforholderadomains
AT duranricardoguillermo weightedpoincareandkorninequalitiesforholderadomains
AT lombardiariell weightedpoincareandkorninequalitiesforholderadomains
_version_ 1768543274560126976

Ejemplares similares