ESTIMATES OF THE GAPS BETWEEN CONSECUTIVE EIGENVALUES OF LAPLACIAN

被引：8

作者：

Chen, Daguang ^{[1
]}

Zheng, Tao ^{[2
]}

Yang, Hongcang ^{[3
]}

机构：

[1] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China

[2] Beijing Inst Technol, Sch Math & Stat, Beijing 100081, Peoples R China

[3] Chinese Acad Sci, Hua Loo Keng Key Lab Math, Beijing 100080, Peoples R China

来源：

PACIFIC JOURNAL OF MATHEMATICS | 2016年 / 282卷 / 02期

关键词：

Laplacian; consecutive eigenvalues; test function; Riemannian manifold; hyperbolic space; PAYNE-POLYA-WEINBERGER; 1ST; 2; EIGENVALUES; SCHRODINGER-OPERATORS; DIRICHLET LAPLACIANS; RIEMANNIAN-MANIFOLDS; N-DIMENSIONS; BOUNDS; INEQUALITIES; CONJECTURE; PROOF;

D O I：

10.2140/pjm.2016.282.293

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For the eigenvalue problem of the Dirichlet Laplacian on a bounded domain in Euclidean space R-n, we obtain estimates for the upper bounds of the gaps between consecutive eigenvalues which are the best possible in terms of the orders of the eigenvalues. Therefore, it is reasonable to conjecture that this type of estimate also holds for the eigenvalue problem on a Riemannian manifold. We give some particular examples.

引用

页码：293 / 311

页数：19

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