Uniqueness results for fully nonlinear degenerate elliptic equations with discontinuous coefficients
Pierpaolo Soravia · Communications on Pure & Applied Analysis · 2006
In this paper we prove the comparison principle for viscosity solutions of second order, degenerate elliptic pdes with a discontinuous, inhomogeneous term having discontinuities on Lipschitz surfaces. It is shown that appropriate sub and supersolutions $u,v$ of a Dirichlet type boundary value problem satisfy $u\leq v$ in $\Omega$. In particular, continuous viscosity solutions are unique. We also give examples of existence results and apply the comparison principle to prove convergence of approximations.