Hostname: page-component-76fb5796d-dfsvx Total loading time: 0 Render date: 2024-04-28T20:04:28.088Z Has data issue: false hasContentIssue false
  • English
  • Français

Universal inequalities for eigenvalues of a system of elliptic equations

Published online by Cambridge University Press:  25 March 2009

Qing-Ming Cheng  and
Hong-Cang Yang
Qing-Ming Cheng
Affiliation:
Department of Mathematics, Faculty of Science and Engineering, Saga University, Saga 840-8502, Japan (cheng@ms.saga-u.ac.jp)
Hong-Cang Yang
Affiliation:
Academy of Mathematics and Systematical Sciences, Chinese Academy of Sciences, Beijing 100080, People's Republic of China (yanghc@math03.math.ac.cn)
Get access Rights & Permissions [Opens in a new window]

Abstract

Let D be a bounded domain in an n-dimensional Euclidean space ℝn. Assume that

are eigenvalues of an eigenvalue problem of a system of n elliptic equations:

In particular, when n=3, the eigenvalue problem describes the behaviour of the elastic vibration. We obtain universal inequalities for eigenvalues of the above eigenvalue problem by making use of a direct and explicit method; our results are sharper than one of Hook. Furthermore, a universal inequality for lower-order eigenvalues of the above eigenvalue problem is also derived.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 139 , Issue 2 , April 2009 , pp. 273 - 285
Copyright
Copyright © Royal Society of Edinburgh 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)