On the Schwarz problem for the Moisil–Teodoresco system

The Schwarz problem for the classical Cauchy–Riemann system in a flat domain is to determine its solution by the known first component of this solution on the boundary of the domain. In this paper, we consider an analog of this problem for the Moisil—Teodorescu system in a three-dimensional domain bounded by a smooth surface. We propose explicit expressions of the kernel and cokernel of this problem in terms of topological invariants of the domain and the kernel and cokernel of the integral representation of solutions of the Moisil—Teodorescu system that are closely related to the Schwarz problem.