Integral equations in a diffraction problem on a locally inhomogeneous medium interface (Q507722)

In the paper under review, the author studies a particular transmission problem for the Helmholtz equation. Such a problem is related to the diffraction of an \(E\)-polarized field on a locally inhomogeneous interface of transparent media. As a first step he proves the unique solvability of the boundary value problem and provides an integral representation formula for the solution. Then he derives an (equivalent) integral equation formulation of the problem and finally shows a solvability theorem for the integral equations.