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arXiv · 1411.4414

The role of the mean curvature in a Hardy-Sobolev trace inequality

Mouhamed Moustapha Fall·Ignace Aristide Minlend·El Hadji Abdoulaye Thiam
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Abstract

The Hardy-Sobolev trace inequality can be obtained via Harmonic extensions on the half-space of the Stein and Weiss weighted Hardy-Littlewood-Sobolev inequality. In this paper we consider a bounded domain and study the influence of the boundary mean curvature in the Hardy-Sobolev trace inequality on the underlying domain. We prove existence of minimizers when the mean curvature is negative at the singular point of the Hardy potential.

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Mouhamed Moustapha Fall, Ignace Aristide Minlend, El Hadji Abdoulaye Thiam. 2014-11-17. The role of the mean curvature in a Hardy-Sobolev trace inequality. https://arxiv.org/abs/1411.4414

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