Universal Bounds for Eigenvalues of a Buckling Problem
Qing-Ming Cheng,Hongcang Yang +1 more
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In this paper, a new method to construct ''nice'' trial functions was introduced and a universal inequality for higher eigenvalues of the buckling problem was derived by making use of the trial functions.Abstract:
In this paper, we investigate an eigenvalue problem for a biharmonic operator on a bounded domain in an n-dimensional Euclidean space, which is also called a buckling problem. We introduce a new method to construct ``nice'' trial functions and we derive a universal inequality for higher eigenvalues of the buckling problem by making use of the trial functions. Thus, we give an affirmative answer for the problem on universal bounds for eigenvalues of the buckling problem, which was proposed by Payne, Polya and Weinberger in [14] and this problem has been mentioned again by Ashbaugh in [1].read more
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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.
Journal ArticleDOI
Inequalities for eigenvalues of a clamped plate problem
Qiaoling Wang,Changyu Xia +1 more
TL;DR: In this article, the eigenvalues of a clamped plate problem on complete manifolds are studied and a universal inequality for the case of warped product manifolds is shown. But the universal inequalities are not applicable to the complete manifold with Ricci curvatures.
Journal ArticleDOI
Estimates for eigenvalues on Riemannian manifolds
Qing-Ming Cheng,Hongcang Yang +1 more
TL;DR: Li and Yau as mentioned in this paper showed that λ k ⩾ 4 π 2 ( ω n vol Ω ) 2 n k 2 n, for k = 1, 2, …, which is sharp in the sense of average.
Journal ArticleDOI
Inequalities for eigenvalues of the drifting Laplacian on Riemannian manifolds
Changyu Xia,Hongwei Xu +1 more
TL;DR: In this paper, the eigenvalues of the drifting Laplacian on compact Riemannian manifolds with boundary (possibly empty) were studied and a general inequality for them was derived.
Book ChapterDOI
A Survey on the Krein–von Neumann Extension, the Corresponding Abstract Buckling Problem, and Weyl-type Spectral Asymptotics for Perturbed Krein Laplacians in Nonsmooth Domains
TL;DR: In this paper, the authors proved the unitary equivalence of the inverse of the Krein-von Neumann extension (on the orthogonal complement of its kernel) of a densely defined, closed, strictly positive operator, ≥ e ℋ for some e > 0 in a Hilbert space 210B to an abstract buckling operator.
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