Mathematical Research Letters

Volume 15, Issue 4, July 2008 pp. 613-622.

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

Authors: Rafael D. Benguria (1), Rupert L. Frank (2), and Michael Loss (3)
Author institution: P. Universidad Católica de Chile (1), Princeton University (2), and Georgia Tech (3)

Summary: 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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