Weighted a priori estimates with powers of the distance function for elliptic equations

Autores
Toschi, Marisa
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Let u be a weak solution of the equation (-Δ)mu = f with Dirichlet boundary conditions in a smooth bounded domain Ω ⊂ ℝn. In this paper, we obtain some estimates for the Green's function associated to this problem. Moreover, under appropriate conditions on p, we prove some weighted Sobolev a priori estimates for the solution u, where the weight is a power of the distance function. This result extends previous work by R. G. Durán and M. Sanmartino ([Indiana Univ. Math. J. 57 (2008), no. 7, 3463-3478] and [Anal. Theory Appl. 26 (2010), no. 4, 339-349]).
Fil: Toschi, Marisa. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Materia
Dirichlet Function
Green Problems
Weighted Sobolev Spaces
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:11336/84066
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/84066
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network_name_str CONICET Digital (CONICET)
spelling Weighted a priori estimates with powers of the distance function for elliptic equationsToschi, MarisaDirichlet FunctionGreen ProblemsWeighted Sobolev Spaceshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let u be a weak solution of the equation (-Δ)mu = f with Dirichlet boundary conditions in a smooth bounded domain Ω ⊂ ℝn. In this paper, we obtain some estimates for the Green's function associated to this problem. Moreover, under appropriate conditions on p, we prove some weighted Sobolev a priori estimates for the solution u, where the weight is a power of the distance function. This result extends previous work by R. G. Durán and M. Sanmartino ([Indiana Univ. Math. J. 57 (2008), no. 7, 3463-3478] and [Anal. Theory Appl. 26 (2010), no. 4, 339-349]).Fil: Toschi, Marisa. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaHeldermann Verlag2015-09info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/zipapplication/pdfhttp://hdl.handle.net/11336/84066Toschi, Marisa; Weighted a priori estimates with powers of the distance function for elliptic equations; Heldermann Verlag; Georgian Mathematical Journal; 22; 3; 9-2015; 427-4331072-947XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1515/gmj-2015-0032info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:26:23Zoai:ri.conicet.gov.ar:11336/84066instacron: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:34982025-10-22 11:26:23.858CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Weighted a priori estimates with powers of the distance function for elliptic equations
title Weighted a priori estimates with powers of the distance function for elliptic equations
spellingShingle Weighted a priori estimates with powers of the distance function for elliptic equations
Toschi, Marisa
Dirichlet Function
Green Problems
Weighted Sobolev Spaces
title_short Weighted a priori estimates with powers of the distance function for elliptic equations
title_full Weighted a priori estimates with powers of the distance function for elliptic equations
title_fullStr Weighted a priori estimates with powers of the distance function for elliptic equations
title_full_unstemmed Weighted a priori estimates with powers of the distance function for elliptic equations
title_sort Weighted a priori estimates with powers of the distance function for elliptic equations
dc.creator.none.fl_str_mv Toschi, Marisa
author Toschi, Marisa
author_facet Toschi, Marisa
author_role author
dc.subject.none.fl_str_mv Dirichlet Function
Green Problems
Weighted Sobolev Spaces
topic Dirichlet Function
Green Problems
Weighted Sobolev Spaces
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Let u be a weak solution of the equation (-Δ)mu = f with Dirichlet boundary conditions in a smooth bounded domain Ω ⊂ ℝn. In this paper, we obtain some estimates for the Green's function associated to this problem. Moreover, under appropriate conditions on p, we prove some weighted Sobolev a priori estimates for the solution u, where the weight is a power of the distance function. This result extends previous work by R. G. Durán and M. Sanmartino ([Indiana Univ. Math. J. 57 (2008), no. 7, 3463-3478] and [Anal. Theory Appl. 26 (2010), no. 4, 339-349]).
Fil: Toschi, Marisa. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
description Let u be a weak solution of the equation (-Δ)mu = f with Dirichlet boundary conditions in a smooth bounded domain Ω ⊂ ℝn. In this paper, we obtain some estimates for the Green's function associated to this problem. Moreover, under appropriate conditions on p, we prove some weighted Sobolev a priori estimates for the solution u, where the weight is a power of the distance function. This result extends previous work by R. G. Durán and M. Sanmartino ([Indiana Univ. Math. J. 57 (2008), no. 7, 3463-3478] and [Anal. Theory Appl. 26 (2010), no. 4, 339-349]).
publishDate 2015
dc.date.none.fl_str_mv 2015-09
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/11336/84066
Toschi, Marisa; Weighted a priori estimates with powers of the distance function for elliptic equations; Heldermann Verlag; Georgian Mathematical Journal; 22; 3; 9-2015; 427-433
1072-947X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/84066
identifier_str_mv Toschi, Marisa; Weighted a priori estimates with powers of the distance function for elliptic equations; Heldermann Verlag; Georgian Mathematical Journal; 22; 3; 9-2015; 427-433
1072-947X
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1515/gmj-2015-0032
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/zip
application/pdf
dc.publisher.none.fl_str_mv Heldermann Verlag
publisher.none.fl_str_mv Heldermann Verlag
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 12.982451

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