Resolutivity of ideal boundary for nonlinear Dirichlet problems
Fumi-Yuki Maeda, Takayori Ono · Journal of the Mathematical Society of Japan · 2000
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.