On a class of nonlinear degenerate elliptic equations in weighted Sobolev spaces

We prove the existence and uniqueness of a weak solution to a Dirichlet boundary value problem for a class of nonlinear degenerate elliptic equations in the setting of weighted Sobolev spaces. Our proof is based on the weighted Sobolev spaces theory and the Browder-Minty theorem. First, we transform the problem into an equivalent operator equation; second, we utilized the Browder-Minty theorem to prove the existence and uniqueness of a weak solution to the considered problem.