ABSTRACT
This chapter discusses the problem of scattering of plane incident waves by an obstacle. It shows how to develop a generalised notion of the Neumann boundary condition and establish existence and uniqueness of solution to our problem. For this purpose, a local compactness result for Ω as well as a corresponding limiting absorption principle for obstacles with rough boundaries are needed. The chapter shows that the scattering phase can be defined by using the trace-class perturbation theory of Birman and Krein and of Yafaev using wave operators. In order to introduce the results, the chapter describes the concepts of Minkowski measure and Minkowski dimension. The chapter also explores whether the scattering obstacle Γ is uniquely determined by s(λ).
