Inequalities for eigenvalues of the biharmonic operator.
Gerald Hile,R.Z Yeh +1 more
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This article is published in Pacific Journal of Mathematics.The article was published on 1984-05-01 and is currently open access. It has received 85 citations till now. The article focuses on the topics: Compact operator & Shift operator.read more
Citations
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Book ChapterDOI
Isoperimetric and universal inequalities for eigenvalues
TL;DR: A review of the known inequalities for the low eigenvalues of the Dirichlet and Neumann Laplacians on bounded domains in Euclidean space can be found in this paper.
Journal ArticleDOI
Estimates on Eigenvalues of Laplacian
Qing-Ming Cheng,Hongcang Yang +1 more
TL;DR: In this article, the eigenvalues of Laplacian on a bounded connected domain in an n-dimensional unit sphere Sn(1) or a compact homogeneous Riemannian manifold were studied.
Journal ArticleDOI
Inequalities for eigenvalues of a clamped plate problem
Qing-Ming Cheng,Hongcang Yang +1 more
TL;DR: In this article, 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, is obtained.
Journal ArticleDOI
Domain-independent upper bounds for eigenvalues of elliptic operators
TL;DR: In this paper, the authors apply the method used by Hile and Protter [2] to a variety of second-order elliptic problems, in particular, to all constant coefficient problems, where the Laplacian is replaced by a more general operator in a Hilbert space.
Journal ArticleDOI
Spectral theory for perturbed Krein Laplacians in nonsmooth domains
TL;DR: In this article, it was shown that the perturbed Krein Laplacian (i.e., the Krein-von Neumann extension of − Δ + V defined on C 0 ∞ ( Ω ) is spectrally equivalent to the buckling of a clamped plate problem.
References
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Journal ArticleDOI
On the ratio of consecutive eigenvalues
Journal ArticleDOI
Bounds for the Third Membrane Eigenvalue
TL;DR: In this paper, the trial functions for i = 1, 2 were introduced and the first two equalities in (1, 2) can be satisfied with a translation to (2, 3).
Journal ArticleDOI
On the Upper Bound for the Ratio of the First Two Membrane Eigenvalues
TL;DR: In this article, it was shown that the inequality λ2/λ1 < 2.6578 is always fulfilled, irrespective of the shape of the membrane, and this was an improvement upon results due to BRANDS, PAYNE, PÓLYA and WEINBERGER.