A domain perturbation problem for the Poisson equation.

we consider an approach based on Functional Analysis and Potential Theory to analyze domain perturbation problems for boundary value problems for nonhomogeneous elliptic equations. We consider the Dirichlet problem for the Poisson equation and show theorems of real analytic dependence upon domain perturbation for the solutions and for the corresponding energy integrals both in a case in which the data in the interior are real analytic and in the case in which the data in the interior are derivatives of H\"{o}lder continuous functions.