Existence issues for a large class of degenerate elliptic equations with nonlinear Hamiltonians

We give sufficient conditions for the existence and uniqueness, in bounded uniformly convex domains $Ω$, of solutions of degenerate elliptic equations depending also on the nonlinear gradient term $H$, in term of the size of $Ω$, of the forcing term $f$ and of $H$. The results apply to a wide class of equations, having as principal part significant examples, e.g. linear degenerate operators, weighted partial trace operators and the homogeneous Monge-Ampère operator.

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