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

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

2003-01-30

arxiv.org/abs/math/0301352v1

Mathematics

Functional Analysis

14 pages, to appear in "Ricerche di Matematica"

Scientific paper

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 $\Omega \subset \Real^n$.

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