On the unique existence of the classical solution to the problem of electromagnetic wave diffraction by an inhomogeneous lossless dielectric body

A vector problem of electromagnetic wave diffraction by an inhomogeneous volumetric body is considered in the classical formulation. The uniqueness theorem for the solution to the boundary value problem for the system of Maxwell’s equations is proven in the case when the permittivity is real and varies jumpwise on the boundary of the body. A vector integro-differential equation for the electric field is considered. It is shown that the operator of the equation is continuously invertible in the space of square-summable vector functions.