On the reduction of the solution of an inverse boundary value problem to the solution of a Fredholm equation (Q1842489)

The author considers the problem of obtaining a finite domain \(D\subset \mathbb{C}\) and a function \(w\) analytic in \(D\) if the boundary values of the function in terms of arc abscissa \(s\) of an unknown contour \(\partial D\) are \(w= w(s)\), \(s\in \langle 0, l\rangle\) under the condition \(w(0)= w(\ell)\), \(| w(s_ 1)- w(s_ 2)|/ | s_ 1- s_ 2|\geq m> 0\), \(| s_ 1- s_ 2|< \ell\). The problem is reduced to the solution of a second kind Fredholm integral equation in the Hölder space.