Existence and uniqueness for viscosity solutions of degenerate quasilinear elliptic equations in rn

The existence and uniqueness of viscosity solutions of possibly degenerate elliptic equations in is considered. The equations treated include ones of the form where λ > 0 and Du is the gradient of u, as well as fully nonlinear generalizations of this equation. Results are obtained relating growth and continuity properties of the nonlinearity H(p) and the forcing term f(x) and (sometimes sharp) uniqueness classes for solutions. Existence is proved in the uniqueness classes.