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

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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 languageEnglish
Pages (from-to)1143-1146
Number of pages4
JournalJournal of Mathematical Analysis and Applications
Volume464
Issue number2
DOIs
Publication statusPublished - 15 Aug 2018

Keywords

  • Analytic functions
  • Dirichlet problem
  • Planar Brownian motion

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