Eigenvalues of Euclidean wedge domains in higher dimensions

Ratzkin, Jesse
September 2011
Calculus of Variations & Partial Differential Equations;Sep2011, Vol. 42 Issue 1/2, p93
Academic Journal
In this paper, we use a weighted isoperimetric inequality to give a lower bound for 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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