On upper bounds for high order Neumann eigenvalues of convex domains in Euclidean space
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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.References
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Additional Information
- Pawel Kröger
- Affiliation: Department of Mathematics, Temple University, Philadelphia, Pennsylvania 19122
- Address at time of publication: Departamento de Matemática, Universidad Técnica Federico Santa María, Valparaiso, Chile
- Email: pkroeger@mat.utfsm.cl
- Received by editor(s): May 1, 1997
- Received by editor(s) in revised form: September 2, 1997
- Published electronically: February 5, 1999
- Communicated by: Christopher Croke
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 1665-1669
- MSC (1991): Primary 35P15; Secondary 58G25
- DOI: https://doi.org/10.1090/S0002-9939-99-04804-2
- MathSciNet review: 1486739