arXiv:1411.4414 Abstract | arXiv Analytics

arXiv:1411.4414 [math.AP]Abstract References Reviews Resources

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

Mouhamed Moustapha Fall, Ignace Aristide Minlend, El hadji Abdoulaye Thiam

Published 2014-11-17Version 1

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.

Comments: 17 pages

Categories: math.AP

Keywords: hardy-sobolev trace inequality, boundary mean curvature, weiss weighted hardy-littlewood-sobolev inequality, singular point, hardy potential

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