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

Zhengchao Ji; Hongwei Xu

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arXiv · 2011.07249

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

Zhengchao Ji·Hongwei Xu

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Abstract

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.

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Zhengchao Ji, Hongwei Xu. 2020-11-14. Lower bounds for eigenvalues of Laplacian operator and the clamped plate problem. https://arxiv.org/abs/2011.07249

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