Abstract
By applying a reflection principle we set up fully explicit representation formulas for the harmonic Green’s function for orthogonal sectors of the annulus of the unit ball of \({\mathbb{R}^n}\). From the harmonic Green’s function we then can determine the Bergman kernel function of Clifford holomorphic functions by applying an appropriate vector differentiation. As a concrete application we give an explicit analytic representation formula of the solutions to an n-dimensional Dirichlet problem in annular shaped domains that arises in the context of heat conduction.
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Financial support from BOF/GOA 01GA0405 of Ghent University gratefully acknowledged. The second author gratefully acknowledges the financial support from the Graduiertenförderkolleg (GFK) of RWTH Aachen University of Technology.
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Constales, D., Grob, D. & Kraußhar, R.S. Explicit Formulas for the Green’s Function and the Bergman Kernel for Monogenic Functions in Annular Shaped Domains in \({\mathbb{R}^{n+1}}\) . Results. Math. 58, 173–189 (2010). https://doi.org/10.1007/s00025-009-0015-7
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DOI: https://doi.org/10.1007/s00025-009-0015-7