# American Institute of Mathematical Sciences

March  2006, 5(1): 213-240. doi: 10.3934/cpaa.2006.5.213

## Uniqueness results for fully nonlinear degenerate elliptic equations with discontinuous coefficients

 1 Università degli Studi di Padova, Dipartimento di Matematica Pura e Applicata, Italy

Received  January 2005 Revised  November 2005 Published  December 2005

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.
Citation: Pierpaolo Soravia. Uniqueness results for fully nonlinear degenerate elliptic equations with discontinuous coefficients. Communications on Pure & Applied Analysis, 2006, 5 (1) : 213-240. doi: 10.3934/cpaa.2006.5.213
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