Marcinkiewicz continuity estimates for infinite energy solutions of some second order elliptic Dirichlet problems

Abstract

Given a non-linear Dirichlet problem, we prove a result of continuous dependence, for both the solution and its gradient, on the zero order term in the case of low Marcinkiewicz summability for the latter, relying on the existence results and estimates recently proved in Boccardo (Ann Mat Pura Appl 188(4):591–601, 2009). As a consequence, solutions obtained as limit of approximations are proved to be unique even in the infinite energy case.