Mathematical problems of the diffraction theory on bodies with irregularly boundary

The asymptotic representation of the electromagnetic field in the vicinity of an edge has been build for several problems of the diffraction theory. Asymptotic representation of the solution in the vicinity of irregularity has been constructed by the method first offered by V. A. Kondrat'ev for solutions of elliptic differential equations. The representation of the electromagnetic field in the vicinity of reentering metal edge in a waveguide, in the vicinity of reentering dielectric edge in a waveguide, the representation of the electromagnetic field for diffraction problem of plane wave on a body with dielectric wedge, for the scalar problem in vicinity of metal-dielectric edge have been obtained.