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

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.

34 pages, minor correction of keywords