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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 $$ F(D^2u,Du,u,x)=f(x)\ \text{ in } \Omega, \quad u=\psi(x)\ \text{ on } \partial\Omega. $$ 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.

35J60Nonlinear elliptic equations
35J25Second order elliptic equations, boundary value problems
35D40Viscosity solutions of PDE
Full Text: DOI
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