Inequalities for eigenvalues of a clamped plate problem
By Qing Cheng, Hongcang Yang. 2006
75 citations recorded by the source corpus.
Let D be a connected bounded domain in an n-dimensional Euclidean space R n . Assume that 0 < λ 1 < λ 2 ≤ ··· ≤λ k ≤··· are eigenvalues of a clamped plate problem or an eigenvalue problem for the Dirichlet biharmonic operator: Then, we give an upper bound of the (k+1)-th eigenvalue λ k+1 in terms of the first k eigenvalues, which is independent of the domain D, that is, we prove the following: Further, a more explicit inequality of eigenvalues is also obtained.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Mechanics of Materials
View Paper: https://www.semanticscholar.org/paper/2394e8675331e8da975132536c32e0ef48f98eb3
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In Applied Mathematics
In Computational Theory and Mathematics
In Mechanics of Materials
Citations in the corpus
- Universal bounds for eigenvalues of the biharmonic operator on Riemannian manifolds (2007, unknown): “Recently, answering a question of Ashbaugh [1], Cheng and Yang [6] proved the following remarkable estimate: λk+1 − 1 k k ∑ i=1 λi ( 8(n + 2) n2 )1/2 1 k k ∑ i=1 ( λi(λk+1 − λi) )1/2 .”
- Estimates for eigenvalues on Riemannian manifolds (2009, background): “On universal estimates for eigenvalues of the clamped plate problem and the buckling problem, the readers can see [5,7] and [9].”
- Lower order eigenvalues of Dirichlet Laplacian (2008, unknown): “[9], [10], [11], [14], [15], [16], [17], [22], [23], [24], [27], [29], [30] and [31]).”