Continuity with respect to the domain for the Laplacian : a survey

Abstract

In this paper, we present several results of continuity with respect to the domain for the solution of problems with the Laplacian. We consider the usual homogeneous Dirichlet problem, then the Poisson problem and, at least, the Neumann problem. Some different kinds of convergence of the domains are taken in account and we always assume the minimum of regularity for the domains.