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Zbl 1193.35054
Sirakov, Boyan
Solvability of uniformly elliptic fully nonlinear PDE. (English)
[J] Arch. Ration. Mech. Anal. 195, No. 2, 579-607 (2010). ISSN 0003-9527; ISSN 1432-0673/e

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.
[Lubomira Softova (Aversa)]

MSC 2000:: *35J60 Nonlinear elliptic equations
35J25 Second order elliptic equations, boundary value problems
35D40

Keywords: elliptic fully nonlinear equations; viscosity solutions; Dirichlet problem

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