Mathematical models for electromagnetic scattering in R3

We consider the problem of electromagnetic scattering in the infinite connected domain Ω⊂R³ with a boundary S. The smooth surface S is assumed to be perfectly conducting. Two cases are considered: (1) S has a finite diameter and S=∪^N_i=1S_i, where each connected component S_i, is either a boundary of a limited domain Ω_i or it is a cut, i.e. a part of the boundary of a limited domain Ω_i (screen); and (2) S is a k-periodic structure in R³, where k=1,2,3, S∩Ω₀=∪^N_i=1S_i, with S_i described above and Ω₀, is a cell of the k-periodic structure. A new approach to the scalar and electromagnetic scattering is presented based on the boundary hypersingular integral equations known in mathematics as pseudodifferential equations