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Inframonogenic functions and their applications in 3-dimensional elasticity theory

Abstract:

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.