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dc.contributor.author
Cejas, María Eugenia  
dc.contributor.author
Duran, Ricardo Guillermo  
dc.date.available
2019-09-27T18:42:53Z  
dc.date.issued
2018-06  
dc.identifier.citation
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  
dc.identifier.issn
0039-3223  
dc.identifier.uri
http://hdl.handle.net/11336/84701  
dc.description.abstract
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.  
dc.format
application/pdf  
dc.language.iso
eng  
dc.publisher
Polish Academy of Sciences. Institute of Mathematics  
dc.rights
info:eu-repo/semantics/openAccess  
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/  
dc.subject
ELLIPTIC EQUATIONS  
dc.subject
WEIGHTED A PRIORI ESTIMATES  
dc.subject.classification
Matemática Pura  
dc.subject.classification
Matemáticas  
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS  
dc.title
Weighted a priori estimates for elliptic equations  
dc.type
info:eu-repo/semantics/article  
dc.type
info:ar-repo/semantics/artículo  
dc.type
info:eu-repo/semantics/publishedVersion  
dc.date.updated
2019-09-27T14:28:05Z  
dc.journal.volume
243  
dc.journal.number
1  
dc.journal.pagination
13-24  
dc.journal.pais
Polonia  
dc.journal.ciudad
Varsovia  
dc.description.fil
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  
dc.description.fil
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  
dc.journal.title
Studia Mathematica  
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/http://www.impan.pl/get/doi/10.4064/sm8704-6-2017  
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.4064/sm8704-6-2017  
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1711.00879