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Decomposition of inframonogenic functions with applications in elasticity theory

Abstract:

In this paper, we consider functions satisfying the sandwich equation (Formula presented.), where (Formula presented.) stands for the Dirac operator in (Formula presented.). Such functions are referred as inframonogenic and represent an extension of the monogenic functions, ie, null solutions of (Formula presented.). In particular, for odd m, we prove that a C2-function is both inframonogenic and harmonic in (Formula presented.) if and only if it can be represented in Ω as (Formula presented.) where f1 and f2 are, respectively, left and right monogenic functions in Ω, while f3 and f4 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 (Formula presented.).