Acta mathematica scientia,Series B ›› 2011, Vol. 31 ›› Issue (4): 1383-1388.doi: 10.1016/S0252-9602(11)60325-1

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ESTIMATES ON EIGENVALUES FOR THE BIHARMONIC OPERATOR ON A BOUNDED DOMAIN IN Hn(−1)

 HUANG Guang-Yue1,2, LI Xin-Xiao2   

  1. 1. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China
    2. Department of Mathematics, Henan Normal University, Xinxiang 453007, China
  • Received:2009-08-13 Revised:2010-03-29 Online:2011-07-20 Published:2011-07-20
  • Supported by:

    This research is supported by NSFC (11001076); Project of Henan Provincial department of Sciences and Technology(092300410143); and NSF of Henan Provincial Education Department (2009A110010; 2010A110008).

Abstract:

In this paper, we consider eigenvalues of the Dirichlet biharmonic operator on a bounded domain in a hyperbolic space. We obtain universal bounds on the (k + 1)th eigenvalue in terms of the first kth eigenvalues independent of the domains.

Key words: universal inequality, eigenvalue, hyperbolic space, clamped plate problem

CLC Number: 

  • 35P15
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