Special Session 76: Viscosity, nonlinearity and maximum principle
Contents
In the spirit of Potential Theory we present an Extended Maximum Principle (EMP) result for viscosity solutions of fully nonlinear second-order elliptic equations $F(D^2u)=0$ by supposing that no boundary condition is given on a set of null Riesz capacity. Next we consider the wide class of uniformly elliptic equations depending on the gradient variable and we analyse in what extent the lower-order terms influence (EMP) with respect to principal part $D^2u$.
As application we show that (EMP) is a powerful tool to treat removable singularities. Finally we extend such results for a class of degenerate elliptic operator which are partial sum of eigenvalues.