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Comptes Rendus Mathématique
Volume 353, n° 8
pages 735-740 (août 2015)
Doi : 10.1016/j.crma.2015.06.001
Received : 20 Mars 2015 ;  accepted : 1 June 2015
The lower and upper bounds of the first eigenvalues for the bi-harmonic operator on manifolds
Bornes inférieures et supérieures des premières valeurs propres de l'opérateur bi-harmonique sur une variété
 

Liuwei Zhang
 Department of Mathematics, Tongji University, Shanghai, 200092, PR China 

Abstract

In this paper, we will estimate the lower bounds and upper bounds of the first eigenvalues for bi-harmonic operators on manifolds through Reilly's and Bochner's formulae, respectively.

The full text of this article is available in PDF format.
Résumé

Dans cette Note, nous donnons des minorants et majorants des premières valeurs propres de l'opérateur bi-harmonique sur une variété riemannienne, compacte, connexe, en utilisant respectivement les formules de Reilly et de Bochner.

The full text of this article is available in PDF format.

 This work is supported by the National Natural Science Foundation of China (No. 11201400).



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