Bounds for ratios of eigenvalues of the Dirichlet Laplacian
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- by Mark S. Ashbaugh and Rafael D. Benguria PDF
- Proc. Amer. Math. Soc. 121 (1994), 145-150 Request permission
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.References
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Additional Information
- © Copyright 1994 American Mathematical Society
- 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