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• W1994481764 abstract "The authors investigate bounds for various combinations of the low eigenvalues of the Laplacian with Dirichlet boundary conditions on a bounded domain $Omega subset mathbb{R}^n $. These investigations continue and expand upon earlier work of Payne, Pólya, Weinberger, Brands, Chiti, and the authors of this present paper. In particular, the authors generalize and extend to the n-dimensional setting various bounds of Payne, Pólya, Weinberger, Brands, and Chiti and examine their consequences and interrelationships in detail. This includes comparing the asymptotic forms of the various bounds as the dimension n becomes large. The authors also present various extensions and consequences of their recent proof of the Payne–Pólya–Weinberger conjecture, including the proof of a second conjecture of Payne, Pólya, and Weinberger under an added symmetry condition." @default.
• W1994481764 created "2016-06-24" @default.
• W1994481764 creator A5040589882 @default.
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• W1994481764 date "1993-11-01" @default.
• W1994481764 modified "2023-09-26" @default.
• W1994481764 title "More Bounds on Eigenvalue Ratios for Dirichlet Laplacians in<i>N</i>Dimensions" @default.
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• W1994481764 doi "https://doi.org/10.1137/0524091" @default.
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