A Nonlinear Partial Differential Equation and Its Viscosity Solutions

Abstract

We study a nonlinear partial differential equation with Lipschitz continuous coefficient functions. Existence and uniqueness of viscosity solutions is proved by approximating with minimizers of variational integrals. The solutions are shown to satisfy a corresponding minimization property. Stability of solutions with respect to small perturbations of the coefficient functions is discussed, and proved for C^2-solutions.