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arXiv · 0705.3833

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

Rafael D. Benguria·Rupert L. Frank·Michael Loss
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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.

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Rafael D. Benguria, Rupert L. Frank, Michael Loss. 2007-05-25. The sharp constant in the Hardy-Sobolev-Maz'ya inequality in the three dimensional upper half-space. https://arxiv.org/abs/0705.3833

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