Quasiregular solutions for systems of hypoelliptic differential equations

The concept of a quasiregular solution is introduced for a special class of systems of linear partial differential equations of first order, considered on the space of continuously differentiable functions. The methods of distribution theory are used to prove the infinite differentiability of the components of quasiregular solutions of the considered systems, and integral representations of potential type are obtained for them. Examples of quasiregular solutions are given for systems of linear equations of elasticity theory.