The sharp constant in the Hardy-Sobolev-Maz'ya inequality in the three dimensional upper half-space

Details The sharp constant in the Hardy-Sobolev-Maz'ya inequality in the three dimensional upper half-space The sharp constant in the Hardy-Sobolev-Maz'ya inequality in the three dimensional upper half-space

2007-05-25

arxiv.org/abs/0705.3833v1

Physics

Mathematical Physics

9 pages

Scientific paper

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.

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