UNIVERSAL BOUNDS FOR EIGENVALUES OF LAPLACIAN OPERATOR WITH ANY ORDER

doi:10.1016/S0252-9602(10)60091-4

数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (3): 939-948.doi: 10.1016/S0252-9602(10)60091-4

UNIVERSAL BOUNDS FOR EIGENVALUES OF LAPLACIAN OPERATOR WITH ANY ORDER

黄广月, 陈文艺

College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China|School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

收稿日期:2007-12-18 修回日期:2008-02-29 出版日期:2010-05-20 发布日期:2010-05-20
基金资助:
This research is supported by NSFC (10471108, 10631020) of China and NSF of Henan Provincial Education Department (2010A110008)

UNIVERSAL BOUNDS FOR EIGENVALUES OF LAPLACIAN OPERATOR WITH ANY ORDER

HUANG Guang-Yue, CHEN Wen-Yi

College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China|School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

Received:2007-12-18 Revised:2008-02-29 Online:2010-05-20 Published:2010-05-20
Supported by:
This research is supported by NSFC (10471108, 10631020) of China and NSF of Henan Provincial Education Department (2010A110008)

摘要/Abstract

摘要：

Let Ω be a connected bounded domain in Rⁿ. Denote by λ_i the i-th eigenvalue of the Laplacian operator with any order p:

{(-?)^p u=λu in Ω,
u=∂u /∂n =…=∂^p-1u / ∂n ^p^-1=0 on ∂Ω.
In this article, we give some expressions for upper bound of the (k+1)-th eigenvalue λ_k+1 in terms of the first k eigenvalues.

关键词: Eigenvalue, Laplacian operator

Abstract:

Let Ω be a connected bounded domain in Rⁿ. Denote by λ_i the i-th eigenvalue of the Laplacian operator with any order p:

Key words: Eigenvalue, Laplacian operator

中图分类号:

35P15

黄广月, 陈文艺. UNIVERSAL BOUNDS FOR EIGENVALUES OF LAPLACIAN OPERATOR WITH ANY ORDER[J]. 数学物理学报(英文版), 2010, 30(3): 939-948.

HUANG Guang-Yue, CHEN Wen-Yi. UNIVERSAL BOUNDS FOR EIGENVALUES OF LAPLACIAN OPERATOR WITH ANY ORDER[J]. Acta mathematica scientia,Series B, 2010, 30(3): 939-948.

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UNIVERSAL BOUNDS FOR EIGENVALUES OF LAPLACIAN OPERATOR WITH ANY ORDER

UNIVERSAL BOUNDS FOR EIGENVALUES OF LAPLACIAN OPERATOR WITH ANY ORDER

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