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.
