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A universal inequality for Neumann eigenvalues of the Laplacian on a convex domain in Euclidean space

Part of: Partial differential equations on manifolds; differential operators Global differential geometry Spectral theory and eigenvalue problems

Published online by Cambridge University Press:  19 September 2023

Kei Funano
Kei Funano*
Affiliation:
Division of Mathematics and Research Center for Pure and Applied Mathematics, Graduate School of Information Sciences, Tohoku University, 6-3-09 Aramaki-Aza-Aoba, Aoba-ku, Sendai 980-8579, Japan
*
e-mail: kfunano@tohoku.ac.jp
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Abstract

We obtain a new upper bound for Neumann eigenvalues of the Laplacian on a bounded convex domain in Euclidean space. As an application of the upper bound, we derive universal inequalities for Neumann eigenvalues of the Laplacian.

Keywords

Neumann eigenvalues of the Laplacianuniversal inequalitiesconvex domain

MSC classification

Primary: 35P15: Estimation of eigenvalues, upper and lower bounds
Secondary: 53C23: Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces 58J50: Spectral problems; spectral geometry; scattering theory
Type
Article
Information
Canadian Mathematical Bulletin , Volume 67 , Issue 1 , March 2024 , pp. 222 - 226
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of The Canadian Mathematical Society

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