Quasilinear elliptic equations and weighted Sobolev-Poincaré inequalities with distributional weights

Benjamin J. Jaye, Vladimir G. Maz'ya, Igor E. Verbitsky

We introduce a class of weak solutions to the quasilinear equation $-{\Delta }_{p}u=\sigma |u{|}^{p-2}u$ in an open set $\Omega \subset {\mathbf{R}}^n$. Here $p>1$, and ${\Delta }_{p}u$ is the $p$-Laplacian operat…