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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:464

Article

Markowsky, Greg¹ 

[1] Monash Univ, Clayton, Vic 3800, Australia

关键词: Dirichlet problem;    Planar Brownian motion;    Analytic functions;   

DOI  :  10.1016/j.jmaa.2018.04.045

来源: Elsevier

【 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.

【 授权许可】

Free