Existence Issues for a Large Class of Degenerate Elliptic Equations with Nonlinear Hamiltonians

For degenerate elliptic equations with a nonlinear gradient term H, in bounded uniformly convex domains Omega, we give sufficient conditions for the existence and uniqueness of solutions in terms of the size of Omega, 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-Ampere operator.

Automated summary

We provide sufficient conditions for the existence and uniqueness of solutions for degenerate elliptic equations with a nonlinear gradient term in bounded uniformly convex domains, depending on the size of the domain, forcing term, and the properties of the nonlinear gradient term H. The results apply to a wide class of equations, including linear degenerate operators, weighted partial trace operators, and the homogeneous Monge-Ampere operator.