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, G., Durán, R.G., Lombardi, A.L.
Formato: JOUR
Materias:
Inequalities
Korn inequality
Non-smooth domains
Poincaré
Boundary conditions
Distance measurement
Standards
Numerical methods
Acceso en línea: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 todo:paper_01704214_v29_n4_p387_Acosta
record_format dspace
spelling todo:paper_01704214_v29_n4_p387_Acosta2023-10-03T15:07:26Z Weighted Poincaré and Korn inequalities for Hölder α domains Acosta, G. Durán, R.G. Lombardi, A.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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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, G.
Durán, R.G.
Lombardi, A.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.
format JOUR
author Acosta, G.
Durán, R.G.
Lombardi, A.L.
author_facet Acosta, G.
Durán, R.G.
Lombardi, A.L.
author_sort Acosta, G.
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
url http://hdl.handle.net/20.500.12110/paper_01704214_v29_n4_p387_Acosta
work_keys_str_mv AT acostag weightedpoincareandkorninequalitiesforholderadomains
AT duranrg weightedpoincareandkorninequalitiesforholderadomains
AT lombardial weightedpoincareandkorninequalitiesforholderadomains
_version_ 1807316912581902336

Ejemplares similares