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

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Analysis as a Life

Part of the book series: Trends in Mathematics ((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.

Dedicated to Prof. H.G.W. Begehr on the occasion of his 80th birthday

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Author information

Authors and Affiliations

  1. Department of Mathematics, Atilim University, Ankara, Turkey

    Ümit Aksoy

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  1. Ümit Aksoy
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Correspondence to Ümit Aksoy .

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Editors and Affiliations

  1. Department of Economics, Belarusian State University, Minsk, Belarus

    Sergei Rogosin

  2. Mathematics Department, Yeditepe University, Ataşehir, Istanbul, Turkey

    Ahmet Okay Çelebi

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Aksoy, Ü. (2019). Dirichlet Problem for Poisson and Bi-Poisson Equations in Clifford Analysis. In: Rogosin, S., Çelebi, A. (eds) Analysis as a Life. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-02650-9_2

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