A counterexample to the "hot spots" conjecture

被引：60

作者：

Burdzy, K ^{[1
]}

Werner, W

机构：

[1] Univ Washington, Seattle, WA 98195 USA

[2] Univ Paris Sud, Orsay, France

来源：

ANNALS OF MATHEMATICS | 1999年 / 149卷 / 01期

关键词：

D O I：

10.2307/121027

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We construct a counterexample to the "hot spots" conjecture; there exists a bounded connected planar domain (with two holes) such that the second eigenvalue of the Laplacian in that domain with Neumann boundary conditions is simple and such that the corresponding eigenfunction attains its strict maximum at an interior point of that domain.

引用

页码：309 / 317

页数：9