Existence and Uniqueness of Scattering Solutions in Non-smooth Domains

Abstract

A short and self-contained proof of the existence of the scattering solution in exterior domains is presented for some class of second order elliptic equations. The method does not use the integral equation; it is based on Fredholm theory and the limiting absorption principle for solutions in the whole space. It covers domains with Lipschitz boundaries, domains satisfying a cone condition, and those with the so-called local compactness property.