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1. CMB 2010 (vol 53 pp. 475)

 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 $H^{1}(\Omega)\to L^{2}(\partial\Omega)$, where $\Omega$ is a bounded smooth domain in $\RR^N$. 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. Keywords:nonlinear boundary conditions, Sobolev trace embeddingCategories:35J65, 35B33