The sharp constant in the Hardy-Sobolev-Maz'ya inequality in the three dimensional upper half-space
Mathematical Physics
2007-05-28 v1 Analysis of PDEs
math.MP
Abstract
It is shown that the sharp constant in the Hardy-Sobolev-Maz'ya inequality on the three dimensional upper half space is given by the Sobolev constant. This is achieved by a duality argument relating the problem to a Hardy-Littlewood-Sobolev type inequality whose sharp constant is determined as well.
Keywords
Cite
@article{arxiv.0705.3833,
title = {The sharp constant in the Hardy-Sobolev-Maz'ya inequality in the three dimensional upper half-space},
author = {Rafael D. Benguria and Rupert L. Frank and Michael Loss},
journal= {arXiv preprint arXiv:0705.3833},
year = {2007}
}
Comments
9 pages