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

  • B. Schneider

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.
Published
25.01.2006
How to Cite
Schneider, B. “Some Properties of a Cauchy-Type Integral for the Moisil-Theodoresco System of Partial Differential Equations”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, no. 1, Jan. 2006, pp. 105–112, https://umj.imath.kiev.ua/index.php/umj/article/view/3436.
Section
Research articles