Viscosity solutions of fully nonlinear second-order elliptic partial differential equations

Abstract

We investigate comparison and existence results for viscosity solutions of fully nonlinear, second-order, elliptic, possibly degenerate equations. These results complement those recently obtained by R. Jensen and H. Ishii. We consider various boundary conditions like for instance Dirichlet and Neumann conditions. We also apply these methods and results to quasilinear Monge-Ampère equations. Finally, we also address regularity questions.