Uniqueness results for fully nonlinear degenerate elliptic equations with discontinuous coefficients

Pierpaolo Soravia

doi:10.3934/cpaa.2006.5.213

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2006, Volume 5, Issue 1: 213-240. Doi: 10.3934/cpaa.2006.5.213

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Uniqueness results for fully nonlinear degenerate elliptic equations with discontinuous coefficients

Pierpaolo Soravia¹

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

Received: December 31, 2004

Revised: October 31, 2005

Published: February 2006

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Abstract

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.

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

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