Abstract
In this chapter we consider a very simple scattering problem corresponding to the scattering of a time-harmonic plane wave by an imperfect conductor. Although the problem is simple compared to most problems in scattering theory, its mathematical resolution took many years to accomplish and was the focus of energy of some of the outstanding mathematicians of the twentieth century, in particular Kupradze, Rellich, Vekua, Müller, and Weyl. Indeed, the solution of the full three-dimensional problem was not fully realized until 1981 (cf. Sect. 9.5 of [54]). Here we will content ourselves with the two-dimensional scalar problem and its solution by the method of integral equations.