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

Greg Markowsky

doi:10.1016/j.jmaa.2018.04.045

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

Greg Markowsky

School of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

1 Citation (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	1143-1146
Number of pages	4
Journal	Journal of Mathematical Analysis and Applications
Volume	464
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2018.04.045
Publication status	Published - 15 Aug 2018

Keywords

Analytic functions
Dirichlet problem
Planar Brownian motion

Access to Document

10.1016/j.jmaa.2018.04.045

Link to publication in Scopus

Cite this

@article{953cce1c8a0140368212ede2cf712eb7,

title = "A remark on the probabilistic solution of the Dirichlet problem for simply connected domains in the plane",

abstract = "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.",

keywords = "Analytic functions, Dirichlet problem, Planar Brownian motion",

author = "Greg Markowsky",

year = "2018",

month = aug,

day = "15",

doi = "10.1016/j.jmaa.2018.04.045",

language = "English",

volume = "464",

pages = "1143--1146",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

publisher = "Elsevier",

number = "2",

}

TY - JOUR

T1 - A remark on the probabilistic solution of the Dirichlet problem for simply connected domains in the plane

AU - Markowsky, Greg

PY - 2018/8/15

Y1 - 2018/8/15

N2 - 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.

AB - 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.

KW - Analytic functions

KW - Dirichlet problem

KW - Planar Brownian motion

UR - http://www.scopus.com/inward/record.url?scp=85046133278&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2018.04.045

DO - 10.1016/j.jmaa.2018.04.045

M3 - Article

AN - SCOPUS:85046133278

VL - 464

SP - 1143

EP - 1146

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

ER -