Korn inequality and divergence operator: Counterexamples and optimality of weighted estimates

The Korn inequality and related results on solutions of the divergence in Sobolev spaces have been widely studied since the pioneering works by Korn and Friedrichs. In particular, it is known that this inequality is valid for Lipschitz domains as well as for the more general class of John domains. O...

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Detalles Bibliográficos
Autores principales: Acosta Rodriguez, Gabriel, Duran, Ricardo Guillermo
Publicado: 2012
Materias:
Bad domains
Divergence operator
Korn inequality
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v141_n1_p217_Acosta
http://hdl.handle.net/20.500.12110/paper_00029939_v141_n1_p217_Acosta
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00029939_v141_n1_p217_Acosta
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spelling paper:paper_00029939_v141_n1_p217_Acosta2023-06-08T14:23:32Z Korn inequality and divergence operator: Counterexamples and optimality of weighted estimates Acosta Rodriguez, Gabriel Duran, Ricardo Guillermo Bad domains Divergence operator Korn inequality The Korn inequality and related results on solutions of the divergence in Sobolev spaces have been widely studied since the pioneering works by Korn and Friedrichs. In particular, it is known that this inequality is valid for Lipschitz domains as well as for the more general class of John domains. On the other hand, a few known counterexamples show that those results are not valid for certain bounded domains having external cusps. The goal of this paper is to give very simple counterexamples for a class of cuspidal domains in ℝ n . Moreover, we show that these counterexamples can be used to prove the optimality of recently obtained results involving weighted Sobolev spaces. © 2012 American Mathematical Society. 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. 2012 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v141_n1_p217_Acosta http://hdl.handle.net/20.500.12110/paper_00029939_v141_n1_p217_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 Bad domains
Divergence operator
Korn inequality
spellingShingle Bad domains
Divergence operator
Korn inequality
Acosta Rodriguez, Gabriel
Duran, Ricardo Guillermo
Korn inequality and divergence operator: Counterexamples and optimality of weighted estimates
topic_facet Bad domains
Divergence operator
Korn inequality
description The Korn inequality and related results on solutions of the divergence in Sobolev spaces have been widely studied since the pioneering works by Korn and Friedrichs. In particular, it is known that this inequality is valid for Lipschitz domains as well as for the more general class of John domains. On the other hand, a few known counterexamples show that those results are not valid for certain bounded domains having external cusps. The goal of this paper is to give very simple counterexamples for a class of cuspidal domains in ℝ n . Moreover, we show that these counterexamples can be used to prove the optimality of recently obtained results involving weighted Sobolev spaces. © 2012 American Mathematical Society.
author Acosta Rodriguez, Gabriel
Duran, Ricardo Guillermo
author_facet Acosta Rodriguez, Gabriel
Duran, Ricardo Guillermo
author_sort Acosta Rodriguez, Gabriel
title Korn inequality and divergence operator: Counterexamples and optimality of weighted estimates
title_short Korn inequality and divergence operator: Counterexamples and optimality of weighted estimates
title_full Korn inequality and divergence operator: Counterexamples and optimality of weighted estimates
title_fullStr Korn inequality and divergence operator: Counterexamples and optimality of weighted estimates
title_full_unstemmed Korn inequality and divergence operator: Counterexamples and optimality of weighted estimates
title_sort korn inequality and divergence operator: counterexamples and optimality of weighted estimates
publishDate 2012
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v141_n1_p217_Acosta
http://hdl.handle.net/20.500.12110/paper_00029939_v141_n1_p217_Acosta
work_keys_str_mv AT acostarodriguezgabriel korninequalityanddivergenceoperatorcounterexamplesandoptimalityofweightedestimates
AT duranricardoguillermo korninequalityanddivergenceoperatorcounterexamplesandoptimalityofweightedestimates
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