Mixed Boundary Value Problems

Abstract

This chapter is devoted to the study of mixed boundary value problems in electromagnetic scattering theory. Mixed boundary value problems typically model scattering by objects that are coated with a thin layer of material on part of the boundary. We shall consider here two main problems: (1) the scattering by a perfect conductor that is partially coated with a thin dielectric layer and (2) scattering by an orthotropic dielectric that is partially coated with a thin layer of highly conducting material. The first problem leads to an exterior mixed boundary value problem for the Helmholtz equation where on the coated part of the boundary the total field satisfies an impedance boundary condition and on the remaining part of the boundary the total field vanishes, while the second problem leads to a transmission problem with mixed transmission-conducting boundary conditions. In this chapter we shall present a mathematical analysis of these two mixed boundary value problems.