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Uniqueness results for fully nonlinear degenerate elliptic equations with discontinuous coefficients

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  • 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.
    Mathematics Subject Classification: Primary: 35B50, 35A05; Secondary: 35J60, 35J70.


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