Estimates for the lowest eigenvalue of magnetic Laplacians

被引：16

作者：

Ekholm, Tomas ^{[1
]}

Kovarik, Hynek ^{[2
]}

Portmann, Fabian ^{[3
]}

机构：

[1] KTH Royal Inst Technol, Stockholm, Sweden

[2] Univ Brescia, I-25121 Brescia, Italy

[3] Univ Copenhagen, DK-1168 Copenhagen, Denmark

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2016年 / 439卷 / 01期

基金：

瑞典研究理事会; 欧洲研究理事会;

关键词：

Magnetic fields; Magnetic Dirichlet Laplacian; Eigenvalues; SCHRODINGER OPERATOR; FIELD; INEQUALITIES; ASYMPTOTICS; STATE;

D O I：

10.1016/j.jmaa.2016.02.073

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove various estimates for the first eigenvalue of the magnetic Dirichlet Laplacian on a bounded, open, simply connected domain in two dimensions. When the magnetic field is constant, we give lower and upper bounds in terms of geometric quantities of the domain. We furthermore prove a lower bound for the first magnetic Neumann eigenvalue in the case of constant magnetic field. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：330 / 346

页数：17

共 26 条

[1] GROUND-STATE OF A SPIN-1-2 CHARGED-PARTICLE IN A 2-DIMENSIONAL MAGNETIC-FIELD [J].