Weighted a priori estimates for elliptic equations

Autores
Cejas, María Eugenia; Durán, 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.
Facultad de Ciencias Exactas
Materia
Matemática
Ciencias Exactas
Elliptic equations
Weighted a priori estimates
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/98015
Acceder
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spelling Weighted a priori estimates for elliptic equationsCejas, María EugeniaDurán, Ricardo GuillermoMatemáticaCiencias ExactasElliptic equationsWeighted a priori estimatesWe 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 A<sub>p</sub>. The argument is a generalization to bounded domains of the one used in R<sup>n</sup> to prove the continuity of singular integral operators in weighted norms. In the case of singular integral operators it is known that the A<sub>p</sub> 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 A<sub>p</sub> class.Facultad de Ciencias Exactas2018info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf13-24http://sedici.unlp.edu.ar/handle/10915/98015enginfo:eu-repo/semantics/altIdentifier/url/https://ri.conicet.gov.ar/11336/84701info:eu-repo/semantics/altIdentifier/url/http://www.impan.pl/get/doi/10.4064/sm8704-6-2017info:eu-repo/semantics/altIdentifier/issn/0039-3223info:eu-repo/semantics/altIdentifier/doi/10.4064/sm8704-6-2017info:eu-repo/semantics/altIdentifier/arxiv/1711.00879info:eu-repo/semantics/altIdentifier/hdl/11336/84701info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-sa/2.5/ar/Creative Commons Attribution-NonCommercial-ShareAlike 2.5 Argentina (CC BY-NC-SA 2.5)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-09-03T10:52:46Zoai:sedici.unlp.edu.ar:10915/98015Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-03 10:52:46.251SEDICI (UNLP) - Universidad Nacional de La Platafalse
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
Matemática
Ciencias Exactas
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
Durán, Ricardo Guillermo
author Cejas, María Eugenia
author_facet Cejas, María Eugenia
Durán, Ricardo Guillermo
author_role author
author2 Durán, Ricardo Guillermo
author2_role author
dc.subject.none.fl_str_mv Matemática
Ciencias Exactas
Elliptic equations
Weighted a priori estimates
topic Matemática
Ciencias Exactas
Elliptic equations
Weighted a priori estimates
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 A<sub>p</sub>. The argument is a generalization to bounded domains of the one used in R<sup>n</sup> to prove the continuity of singular integral operators in weighted norms. In the case of singular integral operators it is known that the A<sub>p</sub> 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 A<sub>p</sub> class.
Facultad de Ciencias Exactas
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 A<sub>p</sub>. The argument is a generalization to bounded domains of the one used in R<sup>n</sup> to prove the continuity of singular integral operators in weighted norms. In the case of singular integral operators it is known that the A<sub>p</sub> 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 A<sub>p</sub> class.
publishDate 2018
dc.date.none.fl_str_mv 2018
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Articulo
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dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://ri.conicet.gov.ar/11336/84701
info:eu-repo/semantics/altIdentifier/url/http://www.impan.pl/get/doi/10.4064/sm8704-6-2017
info:eu-repo/semantics/altIdentifier/issn/0039-3223
info:eu-repo/semantics/altIdentifier/doi/10.4064/sm8704-6-2017
info:eu-repo/semantics/altIdentifier/arxiv/1711.00879
info:eu-repo/semantics/altIdentifier/hdl/11336/84701
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
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Creative Commons Attribution-NonCommercial-ShareAlike 2.5 Argentina (CC BY-NC-SA 2.5)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Creative Commons Attribution-NonCommercial-ShareAlike 2.5 Argentina (CC BY-NC-SA 2.5)
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