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

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.

Full Text (PDF format)

Published 1 January 2008