Existence Results in Weighted Sobolev Spaces for Some Singular Quasilinear Elliptic Equations

Abstract

In this paper, we obtain the existence of a nontrivial solution for a class of singular quasilinear elliptic equations in weighted Sobolev spaces. The proofs rely on Galerkin-type techniques, Brouwer fixed point theorem, and a new weighted compact Sobolev-type embedding theorem established by Shapiro. The equation is one of the most useful sets of Navier-Stokes equations, which describe the motion of viscous fluid substances such as liquids, gases and so on.