WEIGHTED A PRIORI ESTIMATES FOR POISSON EQUATION

DURÁN, RICARDO; SANMARTINO, MARCELA; TOSCHI, MARISA

INDIANA UNIVERSITY MATHEMATICS JOURNAL

INDIANA UNIV MATH JOURNAL

Año: 2008 vol. 57 p. 3463 - 3478

0022-2518

egin{abstract}Let $Omega$ be a bounded domain in $mathbb{R}^n$ with $partial Omegain C^2$ and let $u$ be a solution of the classical Poisson problem in $Omega$; i.e., egin{eqnarray*} left{egin{array}{cc} -Delta u=f&mbox{ in }Omegau=0&mbox{ on }partialOmega end{array} ight. end{eqnarray*}where $fin L^p_omega(Omega)$ and $omega$ is a weight in $A_p$. The main goal of this paper is to prove the following a prioriestimateegin{eqnarray*}|u|_{W^{2,p}_omega(Omega)} le C, |f|_{L^p_omega(Omega)},end{eqnarray*}and to give some applications for weights given by powersof the distance to the boundary. end{abstract}