Existence and Uniqueness of Solution for a Class of Nonlinear Degenerate Elliptic Equations

In this work we are interested in the existence and uniqueness of solutions for the Navier problem associated to the degenerate nonlinear elliptic equations ∆ [ ω1(x)|∆u|∆u + v1(x)|∆u|∆u ] − div [ ω2(x)|∇u|∇u + v2(x)|∇u|∇u ] = f (x)− div(G(x)) in Ω, in the setting of the weighted Sobolev spaces.