Three-dimensional analogue of Kolosov-Muskhelishvili formulae. (English) Zbl 1388.30073
Bernstein, Swanhild (ed.) et al., Modern trends in hypercomplex analysis. Selected papers presented at the session on Clifford and quaternionic analysis at the 10th international ISAAC congress, University of Macau, China, August 3–8, 2015. Basel: Birkhäuser/Springer (ISBN 978-3-319-42528-3/hbk; 978-3-319-42529-0/ebook). Trends in Mathematics, 203-215 (2016).
Summary: In the plane elasticity an effective method of using the holomorphic complex function theory is based on Kolosov-Muskhelishvili formulae. For a three-dimensional case monogenic Clifford functions or regular quaternion functions of a reduced quaternion variable are used. Such functions are solutions of the Moisil-Theodoresco system. In recent papers some variants of three-dimensional Kolosov-Muskhelishvili formulae are obtained but only for star-shaped regions. For applications it is very important to have these formulae for a wider class of domains. We propose the generalized Kolosov-Muskhelishvili formulae in arbitrary simply connected domains with a smooth boundary not only star-shaped, where a notion of harmonic primitive function is used. The method of proving is based on a new theorem about reconstruction of a regular function from a given scalar part.
For the entire collection see [Zbl 1359.30003].
For the entire collection see [Zbl 1359.30003].
MSC:
| 30G35 | Functions of hypercomplex variables and generalized variables |
Keywords:
monogenic Clifford functions; regular quaternionic functions; Moisil-Theodoresco system; representation formulasReferences:
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