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Eigenvalue estimates
on domains in complete noncompact Riemannian manifolds
Daguang Chen, Tao Zheng and Min Lu |
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Vol. 255 (2012), No. 1, 41–54
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Abstract |
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In this paper, we obtain universal inequalities for eigenvalues of the Dirichlet eigenvalue problem of the Laplacian and the clamped plate problem on a bounded domain in an n-dimensional (n ≥ 3) noncompact simply connected complete Riemannian manifold with sectional curvature Sec satisfying −K2 ≤ Sec ≤−k2, where K ≥ k ≥ 0 are constants. When M is ℍn(−1) (n ≥ 3), these inequalities become ones previously found by Cheng and Yang. |
Keywords
Laplacian, the Dirichlet problem, the clamped plate
problem, eigenvalues, the universal inequality
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Mathematical Subject Classification 2010
Primary: 35P15, 58J50, 58G25, 53C42
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Milestones
Received: 18 January 2011
Revised: 26 October 2011
Accepted: 14 November 2011
Published: 14 March 2012
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Authors |
| Daguang Chen | |
| Department of Mathematical
Sciences Tsinghua University Beijing, 100084 China |
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| Tao Zheng | |
| Hua Loo-Keng Key Laboratory of
Mathematics Chinese Academy of Sciences Beijing, 100190 China |
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| Min Lu | |
| Department of Applied
Mathematics Nanjing Audit University Nanjing, 210029 China |
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