Weighted a Priori Estimates for the Poisson Equation

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Let Ω be a bounded domain in R n with C 2 and let u be a solution of the classical Poisson problem in ; i.e., { u = f in , u = 0 on , where f L p ( ) and is a weight in A p . The main goal of this paper is to prove the following a priori estimate u W 2 , p ( ) C f L p ( ), and to give some applicati...

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Detalles Bibliográficos
Autores principales: Durán, Ricardo Guillermo, Sanmartino, Marcela, Toschi, Marisa
Formato: Articulo Preprint
Lenguaje:Inglés
Publicado: 2008
Materias:
Matemática
Poisson equation
Green function
Calderon zigmund theory
Weighted Sobolev spaces
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/99871
https://ri.conicet.gov.ar/11336/93243
http://www.iumj.indiana.edu/oai/2008/57/3427/3427.xml
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
Descripción
Sumario:Let Ω be a bounded domain in R n with C 2 and let u be a solution of the classical Poisson problem in ; i.e., { u = f in , u = 0 on , where f L p ( ) and is a weight in A p . The main goal of this paper is to prove the following a priori estimate u W 2 , p ( ) C f L p ( ), and to give some applications for weights given by powers of the distance to the boundary.

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