2017
Том 69
№ 9

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Some properties of a Cauchy-type integral for the Moisil-Theodoresco system of partial differential equations

Schneider B.

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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.

English version (Springer): Ukrainian Mathematical Journal 58 (2006), no. 1, pp 118-126.

Citation Example: Schneider B. Some properties of a Cauchy-type integral for the Moisil-Theodoresco system of partial differential equations // Ukr. Mat. Zh. - 2006. - 58, № 1. - pp. 105–112.

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