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

Benguria, Rafael D.; Frank, Rupert L.; Loss, Michael

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

Authors

Benguria, Rafael D.

Frank, Rupert L.

Loss, Michael

Description

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.
9 pages