Lower bounds of Cheeger-Osserman type for the first eigenvalue of the n- dimensional fixed membrane problem (Q921573)
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scientific article; zbMATH DE number 4165853
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Lower bounds of Cheeger-Osserman type for the first eigenvalue of the n- dimensional fixed membrane problem |
scientific article; zbMATH DE number 4165853 |
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Lower bounds of Cheeger-Osserman type for the first eigenvalue of the n- dimensional fixed membrane problem (English)
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1990
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We derive new lower bounds for the first eigenvalue of the Laplacian in a bounded n-dimensional domain with Dirichlet boundary conditions. The lower bounds obtained are related to those of \textit{J. Cheeger} [Probl. Analysis, Sympos. in Honor of Salomon Bochner, Princeton Univ. 1969, 195- 199 (1970; Zbl 0212.449)] and \textit{R. Osserman} [Comment. Math. Helv. 52, 545-555 (1977; Zbl 0374.52008)], and they turn out to be sharper when the domain is not too far from being a ball.
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eigenvalues of the Laplacian
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Dirichlet conditions
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membrane problem
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lower bounds for the first eigenvalue
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0.9004158
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0.8908972
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0.8905561
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0.88787025
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0.8810351
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0.8783479
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0.8752748
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