On the Existence of Extremals for the Sobolev Trace Embedding Theorem with Critical Exponent

In this paper, the existence problem is studied for extremals of the Sobolev trace inequality W 1,p (ω)→ L p* (∂Ω), where Ω is a bounded smooth domain in R N , p *= p ( N −1)/( N − p ), is the critical Sobolev exponent, and 1 < p < N . 2000 Mathematics Subject Classification 35J65 (primary), 35B33 (secondary).