Weighted a priori estimates for elliptic equations

Autores
Cejas, María Eugenia; Duran, Ricardo Guillermo
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We give a simpler proof of the a priori estimates obtained by Durán et al. (2008, 2010) for solutions of elliptic problems in weighted Sobolev norms when the weights belong to the Muckenhoupt class Ap. The argument is a generalization to bounded domains of the one used in Rn to prove the continuity of singular integral operators in weighted norms. In the case of singular integral operators it is known that the Ap condition is also necessary for the continuity. We do not know whether this is also true for the a priori estimates in bounded domains but we are able to prove a weaker result when the operator is the Laplacian or a power of it. We prove that a necessary condition is that the weight belongs to the local Ap class.
Fil: Cejas, María Eugenia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina
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
Materia
ELLIPTIC EQUATIONS
WEIGHTED A PRIORI ESTIMATES
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:11336/84701
Acceder
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spelling Weighted a priori estimates for elliptic equationsCejas, María EugeniaDuran, Ricardo GuillermoELLIPTIC EQUATIONSWEIGHTED A PRIORI ESTIMATEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We give a simpler proof of the a priori estimates obtained by Durán et al. (2008, 2010) for solutions of elliptic problems in weighted Sobolev norms when the weights belong to the Muckenhoupt class Ap. The argument is a generalization to bounded domains of the one used in Rn to prove the continuity of singular integral operators in weighted norms. In the case of singular integral operators it is known that the Ap condition is also necessary for the continuity. We do not know whether this is also true for the a priori estimates in bounded domains but we are able to prove a weaker result when the operator is the Laplacian or a power of it. We prove that a necessary condition is that the weight belongs to the local Ap class.Fil: Cejas, María Eugenia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; ArgentinaFil: 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"; ArgentinaPolish Academy of Sciences. Institute of Mathematics2018-06info: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/11336/84701Cejas, María Eugenia; Duran, Ricardo Guillermo; Weighted a priori estimates for elliptic equations; Polish Academy of Sciences. Institute of Mathematics; Studia Mathematica; 243; 1; 6-2018; 13-240039-3223CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.impan.pl/get/doi/10.4064/sm8704-6-2017info:eu-repo/semantics/altIdentifier/doi/10.4064/sm8704-6-2017info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1711.00879info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:44:52Zoai:ri.conicet.gov.ar:11336/84701instacron: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 09:44:52.882CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Weighted a priori estimates for elliptic equations
title Weighted a priori estimates for elliptic equations
spellingShingle Weighted a priori estimates for elliptic equations
Cejas, María Eugenia
ELLIPTIC EQUATIONS
WEIGHTED A PRIORI ESTIMATES
title_short Weighted a priori estimates for elliptic equations
title_full Weighted a priori estimates for elliptic equations
title_fullStr Weighted a priori estimates for elliptic equations
title_full_unstemmed Weighted a priori estimates for elliptic equations
title_sort Weighted a priori estimates for elliptic equations
dc.creator.none.fl_str_mv Cejas, María Eugenia
Duran, Ricardo Guillermo
author Cejas, María Eugenia
author_facet Cejas, María Eugenia
Duran, Ricardo Guillermo
author_role author
author2 Duran, Ricardo Guillermo
author2_role author
dc.subject.none.fl_str_mv ELLIPTIC EQUATIONS
WEIGHTED A PRIORI ESTIMATES
topic ELLIPTIC EQUATIONS
WEIGHTED A PRIORI ESTIMATES
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We give a simpler proof of the a priori estimates obtained by Durán et al. (2008, 2010) for solutions of elliptic problems in weighted Sobolev norms when the weights belong to the Muckenhoupt class Ap. The argument is a generalization to bounded domains of the one used in Rn to prove the continuity of singular integral operators in weighted norms. In the case of singular integral operators it is known that the Ap condition is also necessary for the continuity. We do not know whether this is also true for the a priori estimates in bounded domains but we are able to prove a weaker result when the operator is the Laplacian or a power of it. We prove that a necessary condition is that the weight belongs to the local Ap class.
Fil: Cejas, María Eugenia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina
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
description We give a simpler proof of the a priori estimates obtained by Durán et al. (2008, 2010) for solutions of elliptic problems in weighted Sobolev norms when the weights belong to the Muckenhoupt class Ap. The argument is a generalization to bounded domains of the one used in Rn to prove the continuity of singular integral operators in weighted norms. In the case of singular integral operators it is known that the Ap condition is also necessary for the continuity. We do not know whether this is also true for the a priori estimates in bounded domains but we are able to prove a weaker result when the operator is the Laplacian or a power of it. We prove that a necessary condition is that the weight belongs to the local Ap class.
publishDate 2018
dc.date.none.fl_str_mv 2018-06
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/11336/84701
Cejas, María Eugenia; Duran, Ricardo Guillermo; Weighted a priori estimates for elliptic equations; Polish Academy of Sciences. Institute of Mathematics; Studia Mathematica; 243; 1; 6-2018; 13-24
0039-3223
CONICET Digital
CONICET
url http://hdl.handle.net/11336/84701
identifier_str_mv Cejas, María Eugenia; Duran, Ricardo Guillermo; Weighted a priori estimates for elliptic equations; Polish Academy of Sciences. Institute of Mathematics; Studia Mathematica; 243; 1; 6-2018; 13-24
0039-3223
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.impan.pl/get/doi/10.4064/sm8704-6-2017
info:eu-repo/semantics/altIdentifier/doi/10.4064/sm8704-6-2017
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1711.00879
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 Polish Academy of Sciences. Institute of Mathematics
publisher.none.fl_str_mv Polish Academy of Sciences. Institute of Mathematics
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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