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On a Hypercomplex Version of the Kelvin Solution in Linear Elasticity

  • Sebastian Bock
Conference paper
Part of the Trends in Mathematics book series (TM)

Abstract

The article gives an overview about recently developed spatial generalizations of the Kolosov-Muskhelishvili formulae using the framework of hypercomplex function theory. Based on these results, a hypercomplex version of the classical Kelvin solution is obtained. For this purpose a new class of monogenic functions with (logarithmic) line singularities is studied and an associated two step recurrence formula is proved. Finally, a connection of the function system to the Cauchy-kernel function is established.

Keywords

Recurrence formulae Generalized Kolosov-Muskhelishvili formulae Kelvin solution 

Mathematics Subject Classification (2010)

Primary 30G35; Secondary 74B05 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Mathematics/PhysicsBauhaus-Universität WeimarWeimarGermany

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