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- W1966802697 abstract "In this paper we consider eigenvalues of the Dirichlet biharmonic operator on compact Riemannian manifolds with boundary (possibly empty) and prove a general inequality for them. By using this inequality, we study eigenvalues of the Dirichlet biharmonic operator on compact domains in a Euclidean space or a minimal submanifold of it and a unit sphere. We obtain universal bounds on the ( k + 1 ) th eigenvalue on such objects in terms of the first k eigenvalues independent of the domains. The estimate for the ( k + 1 ) th eigenvalue of bounded domains in a Euclidean space improves an important inequality obtained recently by Cheng and Yang." @default.
- W1966802697 created "2016-06-24" @default.
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- W1966802697 date "2007-04-01" @default.
- W1966802697 modified "2023-09-25" @default.
- W1966802697 title "Universal bounds for eigenvalues of the biharmonic operator on Riemannian manifolds" @default.
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- W1966802697 doi "https://doi.org/10.1016/j.jfa.2006.11.007" @default.
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