Some necessary and some sufficient conditions for the compactness of the embedding of weighted Sobolev spaces

Abstract

We give some necessary conditions and sufficient conditions for the compactness of the embedding of Sobolev spaces $W^{1,p}(\Omega ,w)\to L^p(\Omega ,w),$ where $w$ is some weight on a domain $Ω\subset \Real^n$.

14 pages, to appear in "Ricerche di Matematica"