The Hilbert problem for a first order linear elliptic system with nonfinite coefficients on a Riemann surface with boundary (Q1022220)

Let \(R\) be a compact Riemann surface with boundary. The author studies the Hilbert problem on \(R\) for a first order linear elliptic system with nonfinite coefficients. The author proves that the problem is Neotherian and exactly calculates its winding number (index) \(2\kappa - n(2h+m-2)\), where \(h\) is the genus of \(R\), \(\kappa\) is the winding number of the coefficient of the problem, \(m\) is the number of components of the boundary \(\partial R\). The natural number \(n\) determines the behavior of functions and differentials in a neighborhood of \(\partial R\).