Range of the first three eigenvalues of the planar Dirichlet Laplacian

Details Range of the first three eigenvalues of the planar Dirichlet Laplacian Range of the first three eigenvalues of the planar Dirichlet Laplacian

2002-03-22

arxiv.org/abs/math/0203231v1

Mathematics

Spectral Theory

21 page; 9 figures

Scientific paper

We conduct extensive numerical experiments 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. We also prove some properties of a maximizer of the
ratio $\lambda_3/\lambda_1$.

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