A Nonlinear Partial Differential Equation and Its Viscosity Solutions
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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.