Published 15 Jan 2003. First received 13 Mar 2002.

Range of the first three eigenvalues of the planar Dirichlet Laplacian

Michael Levitin and Rustem Yagudin

Abstract: 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.

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