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On upper bounds for high order Neumann eigenvalues of convex domains in Euclidean space
Author(s):
Pawel
Kröger
Journal:
Proc. Amer. Math. Soc.
127
(1999),
1665-1669.
MSC (1991):
Primary 35P15;
Secondary 58G25
Posted:
February 5, 1999
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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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- Chavel, I., Eigenvalues in Riemannian geometry. Academic Press, Orlando 1984. MR 86g:58140
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- Cheng, S.-Y., Eigenvalue comparison theorems and its geometric applications. Math. Z. 143, 289-297 (1975). MR 51:14170
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- Courant, R.; Hilbert, D., Methods of mathematical physics, vol. I. Interscience, New York 1953. MR 16:426a
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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:
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
Posted:
February 5, 1999
Communicated by:
Christopher Croke
Copyright of article:
Copyright
1999,
American Mathematical Society
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