The Riemann–Hilbert Boundary Value Problem for the Moisil–Theodoresco System

Abstract

We consider the Riemann–Hilbert boundary value problem for the Moisil–Theodoresco system in a multiply connected domain bounded by a smooth surface in the three–dimensional space. We obtain a criterion for the Fredholm property of the problem and a formula for its index æ = m − s, where s is the number of connected components of the boundary and m is the order of the first de Rham cogomology group of the domain. The study is based on the integral representation of a general solution to the Moisil–Theodoresco system and an explicit description of its kernel and cokernel.