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 Estimates for eigenvalues of Neumann and Navier problem Bull. Korean Math. Soc. 2021 Vol. 58, No. 6, 1315-1325 https://doi.org/10.4134/BKMS.b200170Published online November 1, 2021Printed 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 Supported by : http://bkms.kms.or.kr/journal/view.html?doi=10.4134/BKMS.b200170 Downloads: Full-text PDF   Full-text HTML

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