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 the underlying domain. We prove existence of minimizers when the mean curvature is negative at the singular point of the Hardy potential. 
Mouhamed Moustapha Fall, Ignace Aristide Minlend, El Hadji Abdoulaye   Thiam
math.AP