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arXiv · 0905.0199

Eigenvalues of Euclidean wedge domains in higher dimensions

Jesse Ratzkin
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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.

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Jesse Ratzkin. 2009-05-03. Eigenvalues of Euclidean wedge domains in higher dimensions. https://arxiv.org/abs/0905.0199

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