Eigenvalues of Euclidean wedge domains in higher dimensions

Abstract

In this paper, we use a weighted isoperimetric inequality to give a lower bound on the first Dirichlet eigenvalue of the Laplacian on a bounded domain inside a Euclidean cone. Our bound is sharp, in that only sectors realize it. This result generalizes a lower bound of Payne and Weinberger in two dimensions.

arXiv comment10 pages, no figures v2: revised and improved Section 3, to appear in Calculus of Variations and Partial Differential Equation