APPLICATION ON SCHWARZ FUNCTION ON AN INVERSE BOUNDARY VALUE PROBLEM

Abstract

The Schwarz function for the curve is a unique analytic function \(S(z)\), that in every point \(z\) of the curve its value is \(\bar{z}\). The complex equation \(\bar{z}=g(z)\) will be called \(K\)-contour, if it describes closed or non-closed contour or a set of isolated points, when \(g(z)\) is an analytic function. In the case of inverse boundary problem when a simple smooth contour is given, the problem of finding unknown \(K\)-contour and unknown poly-analytic function under the given boundary conditions is solved.