Weighted a priori estimates for elliptic equations

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<...

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Autores principales: Cejas, María Eugenia, Durán, Ricardo Guillermo
Formato: Articulo
Lenguaje:Inglés
Publicado: 2018
Materias:
Matemática
Ciencias Exactas
Elliptic equations
Weighted a priori estimates
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/98015
https://ri.conicet.gov.ar/11336/84701
http://www.impan.pl/get/doi/10.4064/sm8704-6-2017
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-98015
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Matemática
Ciencias Exactas
Elliptic equations
Weighted a priori estimates
spellingShingle Matemática
Ciencias Exactas
Elliptic equations
Weighted a priori estimates
Cejas, María Eugenia
Durán, Ricardo Guillermo
Weighted a priori estimates for elliptic equations
topic_facet Matemática
Ciencias Exactas
Elliptic equations
Weighted a priori estimates
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.
format Articulo
Articulo
author Cejas, María Eugenia
Durán, Ricardo Guillermo
author_facet Cejas, María Eugenia
Durán, Ricardo Guillermo
author_sort Cejas, María Eugenia
title Weighted a priori estimates for elliptic equations
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
publishDate 2018
url http://sedici.unlp.edu.ar/handle/10915/98015
https://ri.conicet.gov.ar/11336/84701
http://www.impan.pl/get/doi/10.4064/sm8704-6-2017
work_keys_str_mv AT cejasmariaeugenia weightedaprioriestimatesforellipticequations
AT duranricardoguillermo weightedaprioriestimatesforellipticequations
bdutipo_str Repositorios
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