Weighted a priori estimates for the Poisson equation Ricardo DuranMarcela SanmartinoMarisa Toschi 42B3542B2035D1034B27Poisson equationGreen functionCalderon-Zygmund theoryweighted Sobolev spaces Let $\Omega$ be a bounded domain in $\mathbb{R}^n$ with $\partial\Omega \in C^2$ and let $u$ be a solution of the classical Poisson problem in $\Omega$; i.e., \[ \begin{cases} -\Delta u = f &\mbox{in }\Omega,\\ u = 0 &\mbox{on }\partial\Omega, \end{cases} \] where $f \in L^p_{\omega}(\Omega)$ and $\omega$ is a weight in $A_p$. The main goal of this paper is to prove the following a priori estimate \[ \|u\|_{W^{2,p}_{\omega}(\Omega)} \le C\|f\|_{L^p_{\omega}(\Omega)}, \] and to give some applications for weights given by powers of the distance to the boundary. Indiana University Mathematics Journal 2008 text pdf 10.1512/iumj.2008.57.3427 10.1512/iumj.2008.57.3427 en Indiana Univ. Math. J. 57 (2008) 3463 - 3478 state-of-the-art mathematics http://iumj.org/access/