Sharp remainder terms of Hardy-Sobolev inequalities

In this paper we shall prove the existence of sharp remainder terms involving singular weight (logR/|x|)-2 for Hardy-Sobolev inequalities of the following type:∫Ω|∇u(x)|2dx≥(n-2/2)2∫Ω|u(x)|2/|(x)|2dx for any u∈W1, 20(Ω), Ω is a bounded domain in Rn, n>2, with 0∈Ω. Here the number of remainder terms depends on the choice of R.