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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/129517It 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 pagesMathematical PhysicsAnalysis of PDEsThe sharp constant in the Hardy-Sobolev-Maz'ya inequality in the three dimensional upper half-spacetext