Definability results for the Poisson equation

Abstract

We show that the solution of the Poisson equation with subanalytic data on a bounded subanalytic domain in the plane without isolated boundary points exists and we prove that the solution is definable in the o-minimal structure R-an,R-exp, provided that the domain has smooth boundary. Moreover, we investigate whether the solution is again subanalytic. At the end, we study polygons as examples of domains with nonsmooth boundary.