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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Author: Pawel Kröger
Journal: Proc. Amer. Math. Soc. 127 (1999), 1665-1669
MSC (1991): Primary 35P15; Secondary 58G25
Published electronically: February 5, 1999
MathSciNet review: 1486739
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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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04804-2
PII: S 0002-9939(99)04804-2
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
Article copyright: © Copyright 1999 American Mathematical Society