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.
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Translated from Problemy Matematicheskogo Analiza97, 2019, pp. 129-153.
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Soldatov, A.P. The Riemann–Hilbert Boundary Value Problem for the Moisil–Theodoresco System. J Math Sci 239, 381–411 (2019). https://doi.org/10.1007/s10958-019-04312-y
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DOI: https://doi.org/10.1007/s10958-019-04312-y