Estimates for eigenvalues of Neumann and Navier problem
Bull. Korean Math. Soc. 2021 Vol. 58, No. 6, 1315-1325
Published online November 1, 2021
Printed November 30, 2021
Yanlin Deng, Feng Du, Lanbao Hou
Hubei University; Hubei University; Hubei University
Abstract : In this paper, we firstly prove some general inequalities for the Neumann eigenvalues for domains contained in a Euclidean $n$-space $\R^n$. Using the general inequalities, we can derive some new Neumann eigenvalues estimates which include an upper bound for the $(k+1)^{th}$ eigenvalue and a new estimate for the gap of the consecutive eigenvalues. Moreover, we give sharp lower bound for the first eigenvalue of two kinds of eigenvalue problems of the biharmonic operator with Navier boundary condition on compact Riemannian manifolds with boundary and positive Ricci curvature.
Keywords : Eigenvalues, Neumann problem, Navier problem, upper bound, lower bound
MSC numbers : Primary 35P15, 53C40
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