Solutions of the divergence and Korn inequalities on domains with an external cusp

Autores
Duran, Ricardo Guillermo; Lopez Garcia, Fernando Alfonso
Año de publicación
2010
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
This paper deals with solutions of the divergence for domains with external cusps. It is known that the classic results in standard Sobolev spaces, which are basic in the variational analysis of the Stokes equations, are not valid for this class of domains. For some bounded domains Ω⊂Rn presenting power type cusps of integer dimension m≤n−2, we prove the existence of solutions of the equation divu=f in weighted Sobolev spaces, where the weights are powers of the distance to the cusp. The results obtained are optimal in the sense that the powers cannot be improved. As an application, we prove existence and uniqueness of solutions of the Stokes equations in appropriate spaces for cuspidal domains. Also, we obtain weighted Korn type inequalities for this class of domains.
Fil: Duran, Ricardo Guillermo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Lopez Garcia, Fernando Alfonso. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Materia
DIVERGENCE OPERATOR
WEIGHTED SOBOLEV SPACES
KORN INEQUALITY
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:11336/68479
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Solutions of the divergence and Korn inequalities on domains with an external cuspDuran, Ricardo GuillermoLopez Garcia, Fernando AlfonsoDIVERGENCE OPERATORWEIGHTED SOBOLEV SPACESKORN INEQUALITYhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1This paper deals with solutions of the divergence for domains with external cusps. It is known that the classic results in standard Sobolev spaces, which are basic in the variational analysis of the Stokes equations, are not valid for this class of domains. For some bounded domains Ω⊂Rn presenting power type cusps of integer dimension m≤n−2, we prove the existence of solutions of the equation divu=f in weighted Sobolev spaces, where the weights are powers of the distance to the cusp. The results obtained are optimal in the sense that the powers cannot be improved. As an application, we prove existence and uniqueness of solutions of the Stokes equations in appropriate spaces for cuspidal domains. Also, we obtain weighted Korn type inequalities for this class of domains.Fil: Duran, Ricardo Guillermo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Lopez Garcia, Fernando Alfonso. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaSuomalainen Tiedeakatemia2010-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/68479Duran, Ricardo Guillermo; Lopez Garcia, Fernando Alfonso; Solutions of the divergence and Korn inequalities on domains with an external cusp; Suomalainen Tiedeakatemia; Annales Academiae Scientiarum Fennicae. Mathematica; 35; 8-2010; 421-4381239-629X1798-2383CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/0906.2775info:eu-repo/semantics/altIdentifier/doi/10.5186/aasfm.2010.3527info:eu-repo/semantics/altIdentifier/url/http://www.acadsci.fi/mathematica/Vol35/DuranLopezGarcia.htmlinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:52:52Zoai:ri.conicet.gov.ar:11336/68479instacron: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 09:52:52.95CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Solutions of the divergence and Korn inequalities on domains with an external cusp
title Solutions of the divergence and Korn inequalities on domains with an external cusp
spellingShingle Solutions of the divergence and Korn inequalities on domains with an external cusp
Duran, Ricardo Guillermo
DIVERGENCE OPERATOR
WEIGHTED SOBOLEV SPACES
KORN INEQUALITY
title_short Solutions of the divergence and Korn inequalities on domains with an external cusp
title_full Solutions of the divergence and Korn inequalities on domains with an external cusp
title_fullStr Solutions of the divergence and Korn inequalities on domains with an external cusp
title_full_unstemmed Solutions of the divergence and Korn inequalities on domains with an external cusp
title_sort Solutions of the divergence and Korn inequalities on domains with an external cusp
dc.creator.none.fl_str_mv Duran, Ricardo Guillermo
Lopez Garcia, Fernando Alfonso
author Duran, Ricardo Guillermo
author_facet Duran, Ricardo Guillermo
Lopez Garcia, Fernando Alfonso
author_role author
author2 Lopez Garcia, Fernando Alfonso
author2_role author
dc.subject.none.fl_str_mv DIVERGENCE OPERATOR
WEIGHTED SOBOLEV SPACES
KORN INEQUALITY
topic DIVERGENCE OPERATOR
WEIGHTED SOBOLEV SPACES
KORN INEQUALITY
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv This paper deals with solutions of the divergence for domains with external cusps. It is known that the classic results in standard Sobolev spaces, which are basic in the variational analysis of the Stokes equations, are not valid for this class of domains. For some bounded domains Ω⊂Rn presenting power type cusps of integer dimension m≤n−2, we prove the existence of solutions of the equation divu=f in weighted Sobolev spaces, where the weights are powers of the distance to the cusp. The results obtained are optimal in the sense that the powers cannot be improved. As an application, we prove existence and uniqueness of solutions of the Stokes equations in appropriate spaces for cuspidal domains. Also, we obtain weighted Korn type inequalities for this class of domains.
Fil: Duran, Ricardo Guillermo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Lopez Garcia, Fernando Alfonso. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
description This paper deals with solutions of the divergence for domains with external cusps. It is known that the classic results in standard Sobolev spaces, which are basic in the variational analysis of the Stokes equations, are not valid for this class of domains. For some bounded domains Ω⊂Rn presenting power type cusps of integer dimension m≤n−2, we prove the existence of solutions of the equation divu=f in weighted Sobolev spaces, where the weights are powers of the distance to the cusp. The results obtained are optimal in the sense that the powers cannot be improved. As an application, we prove existence and uniqueness of solutions of the Stokes equations in appropriate spaces for cuspidal domains. Also, we obtain weighted Korn type inequalities for this class of domains.
publishDate 2010
dc.date.none.fl_str_mv 2010-08
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/11336/68479
Duran, Ricardo Guillermo; Lopez Garcia, Fernando Alfonso; Solutions of the divergence and Korn inequalities on domains with an external cusp; Suomalainen Tiedeakatemia; Annales Academiae Scientiarum Fennicae. Mathematica; 35; 8-2010; 421-438
1239-629X
1798-2383
CONICET Digital
CONICET
url http://hdl.handle.net/11336/68479
identifier_str_mv Duran, Ricardo Guillermo; Lopez Garcia, Fernando Alfonso; Solutions of the divergence and Korn inequalities on domains with an external cusp; Suomalainen Tiedeakatemia; Annales Academiae Scientiarum Fennicae. Mathematica; 35; 8-2010; 421-438
1239-629X
1798-2383
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/0906.2775
info:eu-repo/semantics/altIdentifier/doi/10.5186/aasfm.2010.3527
info:eu-repo/semantics/altIdentifier/url/http://www.acadsci.fi/mathematica/Vol35/DuranLopezGarcia.html
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
dc.publisher.none.fl_str_mv Suomalainen Tiedeakatemia
publisher.none.fl_str_mv Suomalainen Tiedeakatemia
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
_version_ 1842269188209508352
score 13.13397

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