Eigenvalues of Euclidean wedge domains in higher dimensions
Analysis of PDEs
2016-02-02 v2 Differential Geometry
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.
Cite
@article{arxiv.0905.0199,
title = {Eigenvalues of Euclidean wedge domains in higher dimensions},
author = {Jesse Ratzkin},
journal= {arXiv preprint arXiv:0905.0199},
year = {2016}
}
Comments
10 pages, no figures v2: revised and improved Section 3, to appear in Calculus of Variations and Partial Differential Equation