Some inequalities and asymptotic formulas for eigenvalues on Riemannian manifolds

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:376

Article

Liu, Genqian

关键词: Eigenvalue;    Inequality;    Asymptotic formula;    Riemannian manifold;    The Payne conjecture;   

DOI  :  10.1016/j.jmaa.2010.11.002

来源: Elsevier

【 摘 要 】

In this paper, we establish sharp inequalities for four kinds of classical eigenvalues in bounded domains of Riemannian manifolds. We also obtain the Weyl-type asymptotic formulas for the eigenvalues of the buckling and clamped plate problems in bounded domains of Riemannian manifolds. In addition, we give a negative answer to the Payne conjecture for the one-dimensional case. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free