Mixed inverse boundary value problem for a domain of infinite connectivity with periodic boundary (Q1357931)

Let \(L_x= \bigcup_{k=-\infty}^\infty L_z^k\) be a grid of contours in the plane of complex variable \(z=x+iy\). Assume further that it is a boundary of an unbounded domain \(D_z\) of infinite connectivity. In addition, it is assumed that the contour \(L_z^k\) is obtained from a closed Jordan curve \(L_z^0\) of a finite length by means of its translation for the value \(k\tau e^{i\nu}\), \(\tau>0\), \(0\leq\nu< 2\pi\). The authors discuss the following problem: Find a grid of contours \(L_z\) (i.e., the contour \(L_z^0\) and the grid step \(\tau e^{i\nu}\), called period) and a function \(w(z)\) which conformally maps a domain \(D_z\) onto a given domain \(D_w\) and satisfies certain conditions.