Article ID Journal Published Year Pages File Type
4604097 Annales de l'Institut Henri Poincare (C) Non Linear Analysis 2016 42 Pages PDF
Abstract

We consider the question of giving an upper bound for the first nontrivial eigenvalue of the Wentzell–Laplace operator of a domain Ω, involving only geometrical information. We provide such an upper bound, by generalizing Brock's inequality concerning Steklov eigenvalues, and we conjecture that balls maximize the Wentzell eigenvalue, in a suitable class of domains, which would improve our bound. To support this conjecture, we prove that balls are critical domains for the Wentzell eigenvalue, in any dimension, and that they are local maximizers in dimension 2 and 3, using an order two sensitivity analysis. We also provide some numerical evidence.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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