Hardy-Sobolev-Maz'ya inequalities for arbitrary domains

Details Hardy-Sobolev-Maz'ya inequalities for arbitrary domains Hardy-Sobolev-Maz'ya inequalities for arbitrary domains

2011-02-22

arxiv.org/abs/1102.4394v1

Mathematics

Analysis of PDEs

19 pages

Scientific paper

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.

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