On the upper bound of second eigenvalues for uniformly elliptic operators of any orders.
type: Item
instance of: scholarly article
title: On the upper bound of second eigenvalues for uniformly elliptic operators of any orders.
zbMATH Open document ID: 1035.35086
author: Gao Jia
author: Chunlin Qian
author: Xiao-Ping Yang
published in: Acta Mathematicae Applicatae Sinica. English Series
publication date: 2003-01-01T00:00:00Z
review text: The paper deals with inequalities between the first and second eigenvalue of the following eigenvalue problem \[ (-1)^t \sum_{i_1,i_2,\dots, i_t=1}^m D_{i_1i_2\dots i_t}(a_{i_1i_2\dots i_t}(x)D_{i_1i_2\dots i_t}u)=\lambda(-\Delta)^ru, \;\;x \in \Omega, \] \[ u=\frac{\partial u}{\partial \nu}= \dots = \frac{\partial^{t-1}u}{\partial \nu^{t-1}} =0, \;\;x \in \partial \Omega, \] where \(\Omega \subset R^m\) is a bounded domain. The results are generalizations of the inequalities proven by \textit{Z. Chen} and \textit{C. Qian} [J. Math. Anal. Appl. 186, 821--834 (1994; Zbl 0814.35082)]
reviewed by: Bodo Dittmar
Mathematics Subject Classification ID: 35P15
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 1916598
zbMATH Keywords: eigenvalues
zbMATH Keywords: upper bounds
MaRDI profile type: Publication
full work available at URL: s10255-003-0086-2
OpenAlex ID: W1999976185
cites work: On the difference of consecutive eigenvalues of uniformly elliptic operators of higher orders
cites work: On the upper bound of eigenvalues for elliptic equations with higher orders
cites work: Inequalities for eigenvalues of the biharmonic operator
cites work: Can One Hear the Shape of a Drum? Revisited
DOI: 10.1007/S10255-003-0086-2
description: scientific article; zbMATH DE number 1916598