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Uniqeness results for fully nonlinear degenerate elliptic equations with discontinuous coefficients. (English) Zbl 1132.35324

Summary: 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.

MSC:

35B50 Maximum principles in context of PDEs
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35J60 Nonlinear elliptic equations
35J70 Degenerate elliptic equations
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