Abstract
Our main interest is an analog of a Cauchy-type integral for the theory of the Moisil-Theodoresco system of differential equations in the case of a piecewise-Lyapunov surface of integration. The topics of the paper concern theorems that cover basic properties of this Cauchy-type integral: the Sokhotskii-Plemelj theorem for it as well as a necessary and sufficient condition for the possibility of extending a given Hölder function from such a surface up to a solution of the Moisil-Theodoresco system of partial differential equations in a domain. A formula for the square of a singular Cauchy-type integral is given. The proofs of all these facts are based on intimate relations between the theory of the Moisil-Theodoresco system of partial differential equations and some versions of quaternionic analysis.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 1, pp. 105–112, January, 2006.
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Schneider, B. Some properties of a Cauchy-type integral for the Moisil-Theodoresco system of partial differential equations. Ukr Math J 58, 118–126 (2006). https://doi.org/10.1007/s11253-006-0054-0
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DOI: https://doi.org/10.1007/s11253-006-0054-0