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

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

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...

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Veröffentlicht in:Nonlinear differential equations and applications 2015-10, Vol.22 (5), p.1047-1066
Hauptverfasser: Fall, Mouhamed Moustapha, Minlend, Ignace Aristide, Thiam, El Hadji Abdoulaye
Format: Artikel
Sprache:eng
Schlagworte:
Analysis
Mathematics
Mathematics and Statistics
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Zusammenfassung: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.
ISSN:1021-9722
1420-9004
DOI:10.1007/s00030-015-0313-6