An idea on proving weighted Sobolev embeddings

Details An idea on proving weighted Sobolev embeddings An idea on proving weighted Sobolev embeddings

2010-07-20

arxiv.org/abs/1007.3525v1

Mathematics

Functional Analysis

Scientific paper

This article contains a characterization of when certain weighted Sobolev spaces on $\Bbb R^n$ embed compactly into $L^2(\mathbb R^n, \varphi)$. The characterization is in terms of derivatives of the weight function $\varphi$ and involves the Wiener capacity, as it is obtained from reformulating the problem in terms of resolvent properties of Schr\"odinger operators. This reformulation also works for general domains.

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