A lower bound for sums of eigenvalues of the Laplacian

被引：60

作者：

Melas, AD ^{[1
]}

机构：

[1] Univ Athens, Dept Math, Athens 15784, Greece

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2003年 / 131卷 / 02期

关键词：

D O I：

10.1090/S0002-9939-02-06834-X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let lambda(k)(Omega) be the kth Dirichlet eigenvalue of a bounded domain Omega in R-n. According to Weyl's asymptotic formula we have lambda(k)(Omega) similar to C-n (k/V(Omega))(2/n). The optimal in view of this asymptotic relation lower estimate for the sums Sigma(j=1)(k)lambda(j)(Omega) has been proven by P. Li and S. T. Yau ( Comm. Math. Phys. 88 ( 1983), 309-318). Here we will improve this estimate by adding to its right-hand side a term of the order of k that depends on the ratio of the volume to the moment of inertia of Omega.

引用

页码：631 / 636

页数：6

共 6 条

[1] ESTIMATES FOR SUMS OF EIGENVALUES OF THE LAPLACIAN [J].