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On uniqueness and existence of viscosity solutions of fully nonlinear second-order elliptic PDE’s. (English) Zbl 0645.35025
We prove several comparison and existence theorems for viscosity solutions of fully nonlinear degenerate elliptic equations. One of them extends some recent uniqueness results by Jensen. Some establish the uniqueness of solutions for second order Isaacs’ equations and hence include the uniqueness results for Bellman equations by P.-L. Lions. Our comparison results apply even for discontinuous solutions, and so Perron’s method readily yields the existence of continuous solutions.
Reviewer: H.Ishii

35J60 Nonlinear elliptic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35J15 Second-order elliptic equations
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