On the existence of extremals for the Sobolev trace embedding theorem with critical exponent

Abstract

In this paper, the existence problem is studied for extremals of the Sobolev trace inequality W-1,W-p(Omega) --> L-p* (partial derivativeOmega), where Omega is a bounded smooth domain in R-N, p(*) = p(N - 1)/(N - p) is the critical Sobolev exponent, and 1 < p < N.