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

Autores
Acosta Rodriguez, Gabriel; Duran, Ricardo Guillermo; Lopez Garcia, Fernando Alfonso
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
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 Rn. Moreover, we show that these counterexamples can be used to prove the optimality of recently obtained results involving weighted Sobolev spaces.
Fil: Acosta Rodriguez, Gabriel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Duran, Ricardo Guillermo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Lopez Garcia, Fernando Alfonso. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
Korn Inequality
Divergence Operator
Bad Domains
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/14883
Acceder
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spelling Korn inequality and divergence operator: Counterexamples and optimality of weighted estimatesAcosta Rodriguez, GabrielDuran, Ricardo GuillermoLopez Garcia, Fernando AlfonsoKorn InequalityDivergence OperatorBad Domainshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The 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 Rn. Moreover, we show that these counterexamples can be used to prove the optimality of recently obtained results involving weighted Sobolev spaces.Fil: Acosta Rodriguez, Gabriel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Duran, Ricardo Guillermo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Lopez Garcia, Fernando Alfonso. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaAmerican Mathematical Society2013-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/14883Acosta Rodriguez, Gabriel; Duran, Ricardo Guillermo; Lopez Garcia, Fernando Alfonso; Korn inequality and divergence operator: Counterexamples and optimality of weighted estimates; American Mathematical Society; Proceedings Of The American Mathematical Society; 141; 1; 1-2013; 217-2320002-9939enginfo:eu-repo/semantics/altIdentifier/url/http://www.ams.org/journals/proc/2013-141-01/S0002-9939-2012-11408-X/info:eu-repo/semantics/altIdentifier/doi/10.1090/S0002-9939-2012-11408-Xinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:00:33Zoai:ri.conicet.gov.ar:11336/14883instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 10:00:33.309CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Korn inequality and divergence operator: Counterexamples and optimality of weighted estimates
title Korn inequality and divergence operator: Counterexamples and optimality of weighted estimates
spellingShingle Korn inequality and divergence operator: Counterexamples and optimality of weighted estimates
Acosta Rodriguez, Gabriel
Korn Inequality
Divergence Operator
Bad Domains
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
dc.creator.none.fl_str_mv Acosta Rodriguez, Gabriel
Duran, Ricardo Guillermo
Lopez Garcia, Fernando Alfonso
author Acosta Rodriguez, Gabriel
author_facet Acosta Rodriguez, Gabriel
Duran, Ricardo Guillermo
Lopez Garcia, Fernando Alfonso
author_role author
author2 Duran, Ricardo Guillermo
Lopez Garcia, Fernando Alfonso
author2_role author
author
dc.subject.none.fl_str_mv Korn Inequality
Divergence Operator
Bad Domains
topic Korn Inequality
Divergence Operator
Bad Domains
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv 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 Rn. Moreover, we show that these counterexamples can be used to prove the optimality of recently obtained results involving weighted Sobolev spaces.
Fil: Acosta Rodriguez, Gabriel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Duran, Ricardo Guillermo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Lopez Garcia, Fernando Alfonso. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
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 Rn. Moreover, we show that these counterexamples can be used to prove the optimality of recently obtained results involving weighted Sobolev spaces.
publishDate 2013
dc.date.none.fl_str_mv 2013-01
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/14883
Acosta Rodriguez, Gabriel; Duran, Ricardo Guillermo; Lopez Garcia, Fernando Alfonso; Korn inequality and divergence operator: Counterexamples and optimality of weighted estimates; American Mathematical Society; Proceedings Of The American Mathematical Society; 141; 1; 1-2013; 217-232
0002-9939
url http://hdl.handle.net/11336/14883
identifier_str_mv Acosta Rodriguez, Gabriel; Duran, Ricardo Guillermo; Lopez Garcia, Fernando Alfonso; Korn inequality and divergence operator: Counterexamples and optimality of weighted estimates; American Mathematical Society; Proceedings Of The American Mathematical Society; 141; 1; 1-2013; 217-232
0002-9939
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.ams.org/journals/proc/2013-141-01/S0002-9939-2012-11408-X/
info:eu-repo/semantics/altIdentifier/doi/10.1090/S0002-9939-2012-11408-X
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Mathematical Society
publisher.none.fl_str_mv American Mathematical Society
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.13397

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