Properties of solutions to some weighted p-Laplacian equation

Abstract

In this paper, we prove some qualitative properties for the positive solutions to some degenerate elliptic equation given by \[-\text{div}\big(w|\nabla u|^{p-2}\nabla u\big)=f(x,u),\quad w\in \mathcal{A}_p,\] on smooth domain and for varying nonlinearity \(f\).

Keywords

• \(p\)-laplacian
• degenerate elliptic equations
• weighted sobolev space