Eigenvalues of Euclidean wedge domains in higher dimensions

Details Eigenvalues of Euclidean wedge domains in higher dimensions Eigenvalues of Euclidean wedge domains in higher dimensions

2009-05-03

arxiv.org/abs/0905.0199v2

Mathematics

Analysis of PDEs

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

Scientific paper

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.

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