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Range of the First Three Eigenvalues of the Planar Dirichlet Laplacian

Published online by Cambridge University Press:  01 February 2010

Michael Levitin  and
Rustem Yagudin
Michael Levitin
Affiliation:
Department of Mathematics, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, U. K.M. Levitin@ma.hw.ac.uk, http://www.ma.hw.ac.uk/~levitin
Rustem Yagudin
Affiliation:
Department of Mathematics, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, U. K.

Abstract

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Extensive numerical experiments have been conducted by the authors, aimed at finding the admissible range of the ratios of the first three eigenvalues of a planar Dirichlet Laplacian. The results improve the previously known theoretical estimates of M. Ashbaugh and R. Benguria. Some properties of a maximizer of the ratio λ3/λ1 are also proved in the paper.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 6 , 2003 , pp. 1 - 17
Copyright
Copyright © London Mathematical Society 2003

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