Local and global maxima for the expectation of the lifetime of a Brownian motion on the disk

被引：0
作者：
Bodo Dittmar
机构：
[1] Martin-Luther-Universität Halle-Wittenberg,Naturwissenschaftliche Fakultät III, Institut für Mathematik
来源：
Journal d'Analyse Mathématique | 2008年 / 104卷
关键词：
Brownian Motion; Unit Disk; Elliptic System; Global Maximum; Convex Domain;
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摘要：
The quotient of the iterated Green’s function and the Green’s function ∫DGD(z, ξ)GD(ζ, ξ)dAξ/GD(z, ζ), which is also called the 3G-expression, plays a fundamental role in potential theory and in the theory of Brownian motion. Recently, Dall’acqua, Grunau and Sweers [5] proved that for the unit disk, the 3G-expression cannot obtain its maximum at interior points. The aim of this paper is to give another proof of this result using only elementary conformal mapping techniques.
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