Isoperimetric estimates for the first Neumann eigenvalue of Hermite differential equations

Abstract

We provide isoperimetric Szegö-Weinberger type inequalities for the first nontrivial Neumann eigenvalue ${\mu }_1(\Omega )$ in Gauss space, where $\Omega$ is a possibly unbounded domain of ${\mathbb{R}}^N$. Our main result consists in showing that among all sets of ${\mathbb{R}}^N$ symmetric about the origin, having prescribed Gaussian measure, ${\mu }_1(\Omega )$ is maximum if and only if $\Omega$ is the euclidean ball centered at the origin.

References in corpus (2)

• Maximizing Neumann fundamental tones of triangles
• A second eigenvalue bound for the Dirichlet Schroedinger operator