Inequalities between Dirichlet and Neumann Eigenvalues on the Heisenberg Group

被引：12

作者：

Frank, Rupert L. ^{[1
]}

Laptev, Ari ^{[2
,3
]}

机构：

[1] Princeton Univ, Dept Math, Princeton, NJ 08544 USA

[2] Univ London Imperial Coll Sci Technol & Med, Dept Math, London SW7 2AZ, England

[3] Royal Inst Technol, Dept Math, S-10044 Stockholm, Sweden

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2010年 / 2010卷 / 15期

基金：

美国国家科学基金会;

关键词：

DOMAINS;

D O I：

10.1093/imrn/rnp230

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that for any domain in the Heisenberg group the (k+1)th Neumann eigenvalue of the sub-Laplacian is strictly less than the kth Dirichlet eigenvalue. As a byproduct, we obtain similar inequalities for the Euclidean Laplacian with a homogeneous magnetic field.

引用

页码：2889 / 2902

页数：14

共 17 条

[1]

[Anonymous], 2008, SPECTRAL THEORY DIFF

[2] SYMMETRY THEOREMS RELATED TO POMPEIUS PROBLEM [J].