Compactness and existence results for the $p$-Laplace equation

Marino Badiale, Michela Guida, Sergio Rolando

Given $1<p<N$ and two measurable functions $V\left(r\right)\ge 0$ and $K\left(r\right)>0$, $r>0$, we define the weighted spaces \[ W=\left\{ u\in D^{1,p}(\mathbb{R}^{N}):\int_…