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Solvability of uniformly elliptic fully nonlinear PDE. (English) Zbl 1193.35054

The author studies uniqueness and non-uniqueness of viscosity solutions of uniformly elliptic fully nonlinear equations of the Hamilton-Jacobi-Bellman-Isaacs type

F(D 2 u,Du,u,x)=f(x)inΩ,u=ψ(x)onΩ·

with unbounded ingredients and quadratic growth in the gradient without hypotheses of convexity or properness. Some of the presented results are new even for equations in divergence form.

MSC:
35J60Nonlinear elliptic equations
35J25Second order elliptic equations, boundary value problems
35D40Viscosity solutions of PDE
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