Hardy-Sobolev-Maz'ya inequalities for arbitrary domains

By Rupert L. Frank, Michael Loss. 2011

50 citations recorded by the source corpus.

We prove a Hardy-Sobolev-Maz’ya inequality for arbitrary domains Ω ⊂ R^N with a constant depending only on the dimension N ≥ 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 Schrodinger operators on domains.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ad12a2b6337372c753d30f62a6f6a27fc6551fda

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In Applied Mathematics

1. Junfang Li
2. R. Lewis
3. Yanyan Li
4. Jingang Xiong
5. Tianling Jin
6. Lei Zhang
7. Wolfgang Reichel
8. Luis Caffarelli

In Computational Theory and Mathematics

1. Junfang Li
2. R. Lewis
3. Yanyan Li
4. Lei Zhang
5. Jingang Xiong
6. Tianling Jin
7. Aobing Li
8. Luis Caffarelli

In Mathematical Physics

1. Junfang Li
2. R. Lewis
3. Yanyan Li
4. Haigang Li

Citations in the corpus

• A geometric characterization of a sharp Hardy inequality (2011, methodology): “ated by Tertikas and Tintarev in [30] for n>3 and by Benguria, Frank, and Loss in [6] for n= 3. When n= 2, a Hardy-Moser-Trudinger inequality is given by Wang and Ye [34]. Recently, Frank and Loss [20] proved that the constant c( ) in (5.2) with q= np n p can be replaced by a constant cwhich is i”