Solvability of uniformly elliptic fully nonlinear PDE
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.
scientific article; zbMATH DE number 5675034
scientific article