Some remarks on the nonlinear mixed Cherepanov boundary value problem

We study the existence and properties of holomorphic solutions of the nonlinear mixed Riemann-Hilbert problem or Cherepanov boundary value problem on the unit disc and given H?lder continuous functions on L and on the problem asks for a continuous function f on , holomorphic on , such that Re(<(a(xi))over bar>f(xi)) = 0 on L and vertical bar f(xi)vertical bar = e(u0(xi)) on partial derivative Delta \ L.