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Dirichlet Problem for Poisson and Bi-Poisson Equations in Clifford Analysis

  • Ümit AksoyEmail author
Chapter
Part of the Trends in Mathematics book series (TM)

Abstract

Dirichlet problems for Poisson equation and a second order linear equation are studied in the unit ball by using an integral representation formula with respect to the Laplacian in the complex Clifford algebra \(\mathbb {C}_m\) for m ≥ 3. Iterating the Green type kernel function, representation of the solution of the bi-Poisson equation with homogeneous Dirichlet condition is presented.

Keywords

Clifford analysis Integral representations Poisson equation 

Mathematics Subject Classification (2010)

Primary 30G35; Secondary 31B10 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsAtilim UniversityAnkaraTurkey

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