A lower bound for sums of eigenvalues of the Laplacian期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

A lower bound for sums of eigenvalues of the Laplacian

Authors:	Antonios D Melas

Institution:	Department of Mathematics, University of Athens, Panepistimiopolis 15784, Athens, Greece

Abstract:	Let $\lambda _{k}(\Omega )$ be the th Dirichlet eigenvalue of a bounded domain $\Omega$ in $\mathbb{R} ^{n}$ . According to Weyl's asymptotic formula we have $\begin{displaymath}\lambda _{k}(\Omega )\thicksim C_{n}(k/V(\Omega ))^{2/n}.\end{displaymath}$ The optimal in view of this asymptotic relation lower estimate for the sums $\sum_{j=1}^{k}\lambda _{j}(\Omega )$ 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 that depends on the ratio of the volume to the moment of inertia of $\Omega$ .

Keywords:

	点击此处可从《Proceedings of the American Mathematical Society》浏览原始摘要信息
	点击此处可从《Proceedings of the American Mathematical Society》下载免费的PDF全文