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

• Autores: Rafael D. Benguria, Rupert L. Frank, Michael Loss
• Localización: Mathematical research letters, ISSN 1073-2780, Vol. 15, Nº 4, 2008, págs. 613-622
• Idioma: inglés
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• Resumen

  • 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.