NEW BOUNDS ON EIGENVUALUES OF LAPLACIAN

doi:10.1007/s10473-019-0217-3

数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (2): 545-550.doi: 10.1007/s10473-019-0217-3

NEW BOUNDS ON EIGENVUALUES OF LAPLACIAN

纪正超

Center of Mathematical Scienses, Zhejiang University, Hangzhou 310027, China

收稿日期:2018-01-07 修回日期:2018-08-01 出版日期:2019-04-25 发布日期:2019-05-06
作者简介:Zhengchao JI,jizhengchao@zju.edu.cn

NEW BOUNDS ON EIGENVUALUES OF LAPLACIAN

Zhengchao JI

Center of Mathematical Scienses, Zhejiang University, Hangzhou 310027, China

Received:2018-01-07 Revised:2018-08-01 Online:2019-04-25 Published:2019-05-06

摘要/Abstract

摘要： In this paper, we investigate non-zero positive eigenvalues of the Laplacian with Dirichlet boundary condition in an n-dimentional Euclidean space Rⁿ, then we obtain an new upper bound of the (k + 1)-th eigenvalue λ_k+1, which improve the previous estimate which was obtained by Cheng and Yang, see (1.8).

关键词: eigenvalues, Laplacian, Euclidean space, recursion formula

Abstract: In this paper, we investigate non-zero positive eigenvalues of the Laplacian with Dirichlet boundary condition in an n-dimentional Euclidean space Rⁿ, then we obtain an new upper bound of the (k + 1)-th eigenvalue λ_k+1, which improve the previous estimate which was obtained by Cheng and Yang, see (1.8).

Key words: eigenvalues, Laplacian, Euclidean space, recursion formula

纪正超. NEW BOUNDS ON EIGENVUALUES OF LAPLACIAN[J]. 数学物理学报(英文版), 2019, 39(2): 545-550.

Zhengchao JI. NEW BOUNDS ON EIGENVUALUES OF LAPLACIAN[J]. Acta mathematica scientia,Series B, 2019, 39(2): 545-550.

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NEW BOUNDS ON EIGENVUALUES OF LAPLACIAN

NEW BOUNDS ON EIGENVUALUES OF LAPLACIAN

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