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

  • Mouhamed Moustapha Fall
  • Ignace Aristide Minlend
  • El Hadji Abdoulaye Thiam
Article
  • 188 Downloads

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.

Mathematics Subject Classification

35B40 35J60 

Keywords

Hardy–Sobolev inequality Weighted trace Sobolev inequality Mean curvature 

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Copyright information

© Springer Basel 2015

Authors and Affiliations

  • Mouhamed Moustapha Fall
    • 1
  • Ignace Aristide Minlend
    • 1
  • El Hadji Abdoulaye Thiam
    • 1
  1. 1.African Institute for Mathematical Sciences (A.I.M.S.) of SenegalMbourSenegal

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