THE RIEMANN-HILBERT BOUNDARY VALUE PROBLEM FOR THE MOISIL-THEODORESCO SYSTEM

摘要

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 œ = 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. Bibliography: 26 titles.