Mixed boundary-value problem of diffraction on a wedge dissected by a half plane

We solve the problem of diffraction on a wedge symmetrically dissected by a half plane in the case where the Dirichlet and Neumann boundary conditions are given on the relevant surfaces and construct the integral representation of the Green function for the wedge. In the static case, the exact solution of the problem under consideration is obtained in the explicit form. We also analyze singularities of the fields near the edges.