  This paper considers to the problems of diffraction of electromagnetic waves
on a half-plane, which has a finite inclusion in the form of a Lipschitz curve.
The diffraction problem formulated as boundary value problem for Helmholtz
equations and boundary conditions Dirichlet or Neumann on the boundary, as well
as the radiation conditions at infinity. We carry out research on these
problems in generalized Sobolev spaces. We use the operators of potential type,
that by their properties are analogs of the classical potentials of single and
double layers. We proved the solvability of the boundary value problems of
Dirichlet and Neumann. We have obtained solutions of boundary value problems in
the form of operators of potential type. Boundary problems are reduced to
integral equations of the second kind.
