On the Dirichlet Problem

TL;DR

This paper addresses a specific case of the Dirichlet problem by employing discrete martingale convergence and harmonic function properties to find solutions.

Contribution

It introduces a novel approach combining martingale convergence with harmonic mean value properties to solve a particular Dirichlet problem case.

Findings

Successfully solves a specific Dirichlet problem case

Demonstrates convergence of discrete martingales in harmonic contexts

Provides a new method for boundary value problems

Abstract

Using, as main tool, the convergence theorem for discrete martingales and the mean value property of harmonic functions we solve, a particular case of, Dirichlet problem.