Geometrical Structure of Laplacian Eigenfunctions

被引：240

作者：

Grebenkov, D. S. ^{[1
,2
,3
]}

Nguyen, B. -T. ^{[1
]}

机构：

[1] Ecole Polytech, CNRS, Lab Phys Matiere Condensee, F-91128 Palaiseau, France

[2] CNRS Independent Univ Moscow, Lab Poncelet, Moscow 119002, Russia

[3] St Petersburg State Univ, Chebyshev Lab, St Petersburg 199034, Russia

来源：

SIAM REVIEW | 2013年 / 55卷 / 04期

关键词：

Laplace operator; eigenfunctions; eigenvalues; localization; TIME-DEPENDENT DIFFUSION; QUANTUM WAVE-GUIDES; PARTIAL-DIFFERENTIAL-EQUATIONS; SINGULARLY PERTURBED DOMAIN; NEUMANN BOUNDARY-CONDITIONS; GROUND-STATE EIGENFUNCTION; HEAT-CONTENT ASYMPTOTICS; INVERSE SPECTRAL PROBLEM; WEYL-BERRY CONJECTURE; CONVEX PLANE POLYGONS;

D O I：

10.1137/120880173

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We summarize the properties of eigenvalues and eigenfunctions of the Laplace operator in bounded Euclidean domains with Dirichlet, Neumann, or Robin boundary condition. We keep the presentation at a level accessible to scientists from various disciplines ranging from mathematics to physics and computer sciences. The main focus is placed onto multiple intricate relations between the shape of a domain and the geometrical structure of eigenfunctions.

引用

页码：601 / 667

页数：67

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