A remark on the probabilistic solution of the Dirichlet problem for simply connected domains in the plane

被引：4
|
作者：
Markowsky, Greg [1 ]
机构：
[1] Monash Univ, Clayton, Vic 3800, Australia
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2018年 / 464卷 / 02期
基金：
澳大利亚研究理事会;
关键词：
Dirichlet problem; Planar Brownian motion; Analytic functions;
D O I：
10.1016/j.jmaa.2018.04.045
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A new proof is given of a simple probabilistic lemma which implies the solution of the Dirichlet problem for simply connected domains in the plane. This proof uses the conformal invariance of planar Brownian motion in place of the previously existing measure-theoretic arguments. (C) 2018 Elsevier Inc. All rights reserved.
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页码：1143 / 1146
页数：4
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