First Variations of the Best Sobolev Trace Constant with Respect to the Domain

Autores: Julio Daniel Rossi
Localización: Canadian mathematical bulletin, ISSN 0008-4395, Vol. 51, Nº 1, 2008, págs. 140-145
Idioma: inglés
DOI: 10.4153/cmb-2008-016-5
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Resumen
- 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.