Decomposition of inframonogenic functions with applications in elasticity theory

In this paper, we consider functions satisfying the sandwich equation partial differential x_f partial differential x_=0, where partial differential x_ stands for the Dirac operator in Rm. Such functions are referred as inframonogenic and represent an extension of the monogenic functions, ie, null solutions of partial differential x_. In particular, for odd m, we prove that a C-2-function is both inframonogenic and harmonic in omega subset of Rm if and only if it can be represented in omega asf=f1+f2+f3x_+x_f4,where f(1) and f(2) are, respectively, left and right monogenic functions in omega, 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 Lame-Navier system in R3.