ψ-Hyperholomorphic functions and a Kolosov-Muskhelishvili formula

DOI10.1002/mma.3431zbMath1338.30043OpenAlexW1891718445MaRDI QIDQ2795274

Hung Manh Nguyen, Sebastian Bock, Dmitrii Legatiuk, Klaus Gürlebeck

Publication date: 18 March 2016

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mma.3431

zbMATH Keywords

linear elasticityhyperholomorphic functionsquaternion analysis

Mathematics Subject Classification ID

Classical linear elasticity (74B05) Functions of hypercomplex variables and generalized variables (30G35)

Related Items (12)

Representation of solutions of Lamé-Navier system ⋮ Error estimates for the coupling of analytical and numerical solutions ⋮ Solutions of Lamé-Navier system in ball shell domain ⋮ Boundary value problems for the Lamé-Navier system in fractal domains ⋮ Commutative complex algebras of the second rank with unity and some cases of plane orthotropy. I ⋮ Representations of solutions of Lamé system with real coefficients via monogenic functions in the biharmonic algebra ⋮ Fundamental solutions of the Stokes system in quaternion analysis ⋮ Some remarks on Trefftz type approximations ⋮ Three-dimensional Analogue of Kolosov–Muskhelishvili Formulae ⋮ Integral representation formulas related to the Lamé-Navier system ⋮ Reconstruction of solutions to a generalized Moisil-Teodorescu system in Jordan domains with rectifiable boundary ⋮ On a generalized Lamé-Navier system in \(\mathbb{R}^3\)

Cites Work

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• The use of complex valued functions for the solution of three-dimensional elasticity problems
• On the representation of elastic displacement fields in terms of three harmonic functions
• On the representation of three-dimensional elasticity solutions with the aid of complex valued functions
• Contragenic functions of three variables
• On monogenic series expansions with applications to linear elasticity
• A hypercomplex derivative of monogenic functsions in and its Applications
• Quaternionic ψ-hyperholomorphic functions, singular integral operators and boundary value problems I. ψ-hyperholomorphic function theory
• On a spatial generalization of the Kolosov–Muskhelishvili formulae
• [https://portal.mardi4nfdi.de/wiki/Publication:5649488 Vollst�ndigkeitsbeweis des Dreifunktionenansatzes der linearen Elastizit�tstheorie]
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