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Bounds for ratios of eigenvalues of the Dirichlet Laplacian


Authors: Mark S. Ashbaugh and Rafael D. Benguria
Journal: Proc. Amer. Math. Soc. 121 (1994), 145-150
MSC: Primary 35P15; Secondary 35J05
DOI: https://doi.org/10.1090/S0002-9939-1994-1186125-1
MathSciNet review: 1186125
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Abstract: We use a doubling scheme to derive a bound for the ratio of the $ {2^k}$th eigenvalue to the first for the Dirichlet Laplacian on a bounded domain $ \Omega \subset {\mathbb{R}^n}$. The explicit bounds we obtain derive from the optimal bound $ {({\lambda _2}/{\lambda _1})_\Omega } \leq {({\lambda _2}/{\lambda _1})_{n -{\text{dimensional ball}}}}$ (the Payne-Pólya-Weinberger conjecture) recently proved by us.


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DOI: https://doi.org/10.1090/S0002-9939-1994-1186125-1
Article copyright: © Copyright 1994 American Mathematical Society

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