Resolutivity of ideal boundary for nonlinear Dirichlet problems
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.
- Journal of the Mathematical Society of Japan
Journal of the Mathematical Society of Japan 52(3), 561-581, 2000-07
The Mathematical Society of Japan