On upper bounds for high order Neumann eigenvalues of convex domains in Euclidean space

Kröger, Pawel

doi:10.1090/S0002-9939-99-04804-2

On upper bounds for high order Neumann eigenvalues of convex domains in Euclidean space
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Proc. Amer. Math. Soc. 127 (1999), 1665-1669 Request permission

Abstract:

We derive sharp upper bounds for eigenvalues of the Laplacian under Neumann boundary conditions on convex domains with given diameter in Euclidean space. We use the Brunn-Minkowski theorem in order to reduce the problem to a question about eigenvalues of certain classes of Sturm-Liouville problems.

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