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Decomposition of inframonogenic functions with applications in elasticity theory
Author(s) -
Moreno Garcia Arsenio,
Moreno Garcia Tania,
Abreu Blaya Ricardo,
Bory Reyes Juan
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6015
Subject(s) - mathematics , connection (principal bundle) , operator (biology) , pure mathematics , elasticity (physics) , vector valued function , harmonic function , extension (predicate logic) , mathematical analysis , geometry , materials science , composite material , biochemistry , chemistry , repressor , computer science , transcription factor , gene , programming language
In this paper, we consider functions satisfying the sandwich equation ∂ x _f ∂ x _= 0 , where ∂ x _stands for the Dirac operator in R m . Such functions are referred as inframonogenic and represent an extension of the monogenic functions, ie, null solutions of ∂ x _. In particular, for odd m , we prove that a C 2 ‐function is both inframonogenic and harmonic in Ω ⊂ R m if and only if it can be represented in Ω as f = f 1 + f 2 + f 3x _ + x _ f 4 , where f 1 and f 2 are, respectively, left and right monogenic functions in Ω, while f 3 and f 4 are two‐sided monogenic functions there. Finally, in deriving some applications of our results, we have made use of the deep connection between the class of inframonogenic vector fields and the universal solutions of the Lamé‐Navier system in R 3 .