Szegő-Weinberger type inequalities for symmetric domains with holes

T. V. Anoop, Vladimir Bobkov, Pavel Drabek

Let ${\mu }_2(\Omega )$ be the first positive eigenvalue of the Neumann Laplacian in a bounded domain $\Omega \subset {\mathbb{R}}^N$. It was proved by Szegő for $N=2$ and by Weinberger for $N\ge 2$…