Resumen de First Variations of the Best Sobolev Trace Constant with Respect to the Domain
In this paper we study the best constant of the Sobolev trace embedding H1(Omega) \to L2 (partial Omega), where Omega is a bounded smooth domain in {mathbb R}N. We find a formula for the first variation of the best constant with respect to the domain. As a consequence, we prove that the ball is a critical domain when we consider deformations that preserve volume.
