Existence results for degenerate quasilinear elliptic equations in weighted Sobolev spaces

Abstract

In this paper we are interested in the existence of solutions for Dirichlet problem associated to the degenerate quasilinear elliptic equations $$-\,{\rm div}\, [v(x)\,{\cal A}(x, u, {\nabla}u)] + {\omega}(x){\cal A}_0(x,u(x))= f_0 - \sum_{j=1}^nD_jf_j, \ \ {\rm on } \ \ {\Omega}$$ in the setting of the weighted Sobolev spaces ${\rm W}_0^{1,p}(\Omega,\omega,v)$.