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Lower bounds for eigenvalues of Laplacian operator and the clamped plate problem (2011.07249v2)
Published 14 Nov 2020 in math.DG
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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