Unilateral Problem for Degenerate Elliptic Equations with Measure Data in Anisotropic Weighted Sobolev Spaces

In this paper, we prove some properties and lemmas in weighted anisotropic Sobolev spaces. As an application, we study the following non-coercive degenerate elliptic equation \ array*20l Au + H(x,u,∇ u) = μ \;\,&in \;\;Ω , \\ u = 0&on\;\;∂ Ω , array . where μ belongs to L¹(Ω ) + W^ - 1,p⃗'(Ω ,ω ⃗*) . We establish the existence of solutions for the unilateral problem associated to the strongly nonlinear and non-coercive elliptic equation in the anisotropic weighted Sobolev spaces, and we conclude some regularity results.