Resolutivity of ideal boundary for nonlinear Dirichlet problems

Abstract

We consider a quasi-linear second order elliptic differential equation on a euclidean domain. After developing necessary potential theory for the equation which extends some part of the theories in the book by Heinonen-Kilpeläinen-Martio, we show that the ideal boundary of the Royden type compactification of the domain is resolutive with respect to the Dirichlet problem for the equation.