ABSTRACT

The solutions of a number of well-known boundary value problems of complex analysis (for example, the Riemann boundary value problem) can be found in the form of curvilinear integrals over the boundaries of domains under consideration. In this connection, the classical results on that problems concern domains with rectifiable boundaries only. On the other hand, the boundary value problems themselves make sense for non-rectifiable boundaries, too. This is the reason for recent development of theory of generalized integration over plane non-rectifiable Jordan curves and arcs. The existence of such generalized integrations over non-rectifiable arcs depends on certain geometry properties of the arcs in neighborhoods of their ends. Here we consider the connections of generalized integration and so-called torsions of the path of integration at its end points.

摘要

许多著名的复分析边值问题（例如，黎曼边值问题）的解可以在所考虑域的边界上以曲线积分的形式找到。在这方面，关于该问题的经典结果仅涉及具有可校正边界的域。另一方面，边值问题本身对不可修正的边界也有意义。这就是最近发展平面不可矫正若当曲线和弧上的广义积分理论的原因。这种在不可校正弧上的广义积分的存在取决于弧在其末端附近的某些几何特性。