Determination of classes of data for correct statement of the inverse boundary value problem by means of re-parameterization (Q1398518)

The author studies the correct statement of the inverse boundary value problem by means of re-parametrization. The boundary data \(w (s)=u (s)+iv (s)\) of the inverse boundary value problem is given as the superposition of the complex valued function \(\widetilde w (\sigma)=\widetilde u (\sigma)+i\widetilde v (\sigma)\) which gives a simple closed Lyapunov's contour \(L_w\) with the use of the instrinic parameter \(\sigma\), and the re-parametrization function \(\sigma=\sigma(s)\). It is obtained a sufficient condition of almost convexity of the desired contour \(L_z\) in the case of convex known contour \(L_w\).