Mathematical Research Letters

Volume 15 (2008)

Number 4

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

Pages: 613 – 622

DOI: http://dx.doi.org/10.4310/MRL.2008.v15.n4.a1

Authors

Rafael D. Benguria (P. Universidad Católica de Chile)

Rupert L. Frank (Princeton University)

Michael Loss (Georgia Tech)

Abstract

It is shown that the sharp constant in the Hardy-Sobolev-Maz'ya inequality on the upper half space $\mathbb{H}^3 \subset \mathbb{R}^3$ 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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