Open AccessUniqueness results for fully nonlinear degenerate elliptic equations with discontinuous coefficients
Author(s) -
Pierpaolo Soravia
Publication year - 2006
Publication title -
communications on pure and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.077
H-Index - 42
eISSN - 1553-5258
pISSN - 1534-0392
DOI - 10.3934/cpaa.2006.5.213
Subject(s) - uniqueness , degenerate energy levels , classification of discontinuities , mathematics , mathematical analysis , lipschitz continuity , nonlinear system , dirichlet problem , boundary value problem , viscosity solution , elliptic curve , viscosity , convergence (economics) , discontinuity (linguistics) , weak solution , physics , quantum mechanics , economics , economic growth
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 <= 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