ON A CERTAIN GENERALIZED BOUNDARY VALUE PROBLEM OF FUNCTION THEORY

Tran Van Trian
1977 Demonstratio Mathematica  
Introducticm In this paper we shall discuss a certain boundary value problem which generalizes the problem considered in-[l] by B. Bojarski. •1. Some notations Let D be a (m+1) -multiply connected domain bounded by a finite number of simple Lapunow non-intersecting contours L qI L^,...,]^. We denote by L the union of these contours. As usual, the positive direction on L will be taken such that the domain D remains on the left side. We suppose that the curve L Q contains the other curves and the
more » ... ther curves and the origin of coordinates belongs to the domain D. We denote by the class of functions holomorphic in the domain D, continuous on D + L. The formulation of the problem We shall investigate the following boundary value problem. Find a pair of holomorphic functions { f (z), y(z)}, z)e.K, satisfying the following boundary condition (1) |s2 (t) l » tfcL ' We call the above problem briefly problem II. -261 -
doi:10.1515/dema-1977-0120 fatcat:6nzqyyxii5b5pjgllrvjvdvsny