Existence and Uniqueness Viscosity Solutions of Degenerate Quasilinear Elliptic Equations in R(N). Revision

摘要

The existence and uniqueness of viscosity solutions of possible degenerate elliptic equations in Sub N is considered. For example, the equations treated include ones of the form u+H(Du) - lambda = f(x) in R sub N where lambda > 0 and Du is the gradient of u, as well as fully nonlinear generalizations of this equation. Results are obtained which relate 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. Keywords: Linear differential operators, Coefficients, Theorems. (kr)