On the Fredholm property of the electric field equation in the vector diffraction problem for a partially screened solid (Q507716)

A problem of diffraction of a monochromatic electromagnetic wave on a partially screened anisotropic inhomogeneous dielectric body is considered. The corresponding boundary value problem for the system of Maxwell's equations in an unbounded space is studied in a semi-classical statement. The authors use the potential theory to reduce the original boundary value problem to a system of integro-differential equations. The main result of the paper is that the quadratic form of the obtained matrix integro-differential operator is coercive and the operator itself is Fredholm with zero index.