Hardy-Sobolev-Maz'ya inequalities for arbitrary domains
Analysis of PDEs
2011-02-23 v1 Functional Analysis
Spectral Theory
Abstract
We prove a Hardy-Sobolev-Maz'ya inequality for arbitrary domains \Omega\subset\R^N with a constant depending only on the dimension N\geq 3. In particular, for convex domains this settles a conjecture by Filippas, Maz'ya and Tertikas. As an application we derive Hardy-Lieb-Thirring inequalities for eigenvalues of Schr\"odinger operators on domains.
Cite
@article{arxiv.1102.4394,
title = {Hardy-Sobolev-Maz'ya inequalities for arbitrary domains},
author = {Rupert L. Frank and Michael Loss},
journal= {arXiv preprint arXiv:1102.4394},
year = {2011}
}
Comments
19 pages