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http://dx.doi.org/10.4134/BKMS.b200170

ESTIMATES FOR EIGENVALUES OF NEUMANN AND NAVIER PROBLEM  

Deng, Yanlin (School of Mathematics and Physics Science Jingchu University of Technology and Faculty of Mathematics and Statistics Key Laboratory of Applied Mathematics of Hubei Province Hubei University)
Du, Feng (School of Mathematics and Physics Science Jingchu University of Technology and Faculty of Mathematics and Statistics Key Laboratory of Applied Mathematics of Hubei Province Hubei University)
Hou, Lanbao (School of Mathematics and Physics Science Jingchu University of Technology and Faculty of Mathematics and Statistics Key Laboratory of Applied Mathematics of Hubei Province Hubei University)
Publication Information
Bulletin of the Korean Mathematical Society / v.58, no.6, 2021 , pp. 1315-1325 More about this Journal
Abstract
In this paper, we firstly prove some general inequalities for the Neumann eigenvalues for domains contained in a Euclidean n-space ℝn. 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;
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