Viscosity solutions of second order partial differential equations with boundary conditions on Riemannian manifolds

Abstract

The comparison, uniqueness and existence for viscosity solution to a class of fully nonlinear second order partial differential equations with boundary condition on a finite dimensional Riemannian manifold are studied. Some results regarding the regularity of the boundary are obtained. These results show that every compact manifold with C1,1 boundary satisfies the regularity condition.