Viscosity Solutions of Nonlinear Systems of Degenerated Elliptic Equations of Second Order

Abstract

In this paper, we discuss the viscosity solutions of Dirichiet problem for weakly coupled systems of fully nonlinear second order degenerated elliptic equations. We prove the existence, uniqueness and continuity of solutions by Perron’s method combined with the technique of coupled solutions. Our results generalize those in [9] for the case of general quasi-monotonic systems.