Inframonogenic functions and their applications in 3‐dimensional elasticity theory

Solutions of the sandwich equation ∂x_f∂x_=0, where ∂x_ stands for the first‐order differential operator (called Dirac operator) in the Euclidean space Rm, are known as inframonogenic functions. These functions generalize in a natural way the theory of kernels associated with ∂x_, the nowadays well‐...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2018-07, Vol.41 (10), p.3622-3631
Main Authors: Moreno García, Arsenio, Moreno García, Tania, Abreu Blaya, Ricardo, Bory Reyes, Juan
Format: Article
Language:English
Subjects:
Clifford analysis
Differential equations
Elasticity
Euclidean geometry
Euclidean space
inframonogenic functions
Lamé system
linear elasticity
Operators (mathematics)
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Summary:Solutions of the sandwich equation ∂x_f∂x_=0, where ∂x_ stands for the first‐order differential operator (called Dirac operator) in the Euclidean space Rm, are known as inframonogenic functions. These functions generalize in a natural way the theory of kernels associated with ∂x_, the nowadays well‐known monogenic functions, and can be viewed also as a refinement of the biharmonic ones. In this paper we deepen study the connections between inframonogenic functions and the solutions of the homogeneous Lamé‐Navier system in R3. Our findings allow to shed some new light on the structure of the solutions of this fundamental system in 3‐dimensional elasticity theory.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.4850