Locally uniform approximation by solutions of the classical Dirichlet problem

Abstract

LetU be an open subset of aP-harmonic space. It is shown that the space of solutions of the Dirichlet problem onU is dense with respect to locally uniform convergence in the space of Perron-Wiener-Brelot solutions of the generalized Dirichlet problem if and only if the set of irregular boundary points forU is negligible.