Existence and approximation of solutions for a class of degenerate elliptic equations with Neumann boundary condition

Abstract

In this work we study the equation , where is a degenerate elliptic operator, with Neumann boundary condition in a bounded open set . We prove the existence and uniqueness of weak solutions in the weighted Sobolev space for the Neumann problem. The main result establishes that a weak solution of degenerate elliptic equations can be approximated by a sequence of solutions for non-degenerate elliptic equations