arXiv:2011.07249 Abstract | arXiv Analytics

arXiv:2011.07249 [math.DG]Abstract References Reviews Resources

Lower bounds for eigenvalues of Laplacian operator and the clamped plate problem

Published 2020-11-14Version 1

In this paper, we give some lower bounds for several eigenvalues. Firstly, we investigate the eigenvalues $\lambda_i$ of the Laplace operator and prove a sharp lower bound. Moreover, we extent this estimate of the eigenvalues to general cases. Secondly, we study the eigenvalues $\Gamma_i$ for the clamped plate problem and deliver a sharp bound for the clamped plate problem for arbitrary dimension.

Comments: 34 pages

Categories: math.DG

Keywords: clamped plate problem, laplacian operator, eigenvalues, sharp lower bound, arbitrary dimension

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