Scaling coupling of reflecting Brownian motions and the hot spots problem

被引：34

作者：

Pascu, MN ^{[1
]}

机构：

[1] Univ Connecticut, Dept Math, Storrs, CT 06269 USA

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2002年 / 354卷 / 11期

关键词：

coupling of diffusions; reflecting Brownian motion; hot spots conjecture; eigenfunctions; Neumann problem; Laplacian;

D O I：

10.1090/S0002-9947-02-03020-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce a new type of coupling of reflecting Brownian motions in smooth planar domains, called scaling coupling. We apply this to obtain monotonicity properties of antisymmetrc second Neumann eigenfunctions of convex planar domains with one line of symmetry. In particular, this gives the proof of the hot spots conjecture for some known types of domains and some new ones.

引用

页码：4681 / 4702

页数：22

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