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In this paper we examine necessary conditions for an inhomogeneity to benon-scattering, or equivalently, by negation, sufficient conditions for it tobe scattering. These conditions are formulated in terms of the regularity ofthe boundary of the inhomogeneity. We examine broad classes of incident wavesin both two and three dimensions. Our analysis is greatly influenced by theanalysis carried out by Williams [28] in order to establish that a domain,which does not possess the Pompeiu Property, has a real analytic boundary. Thatanalysis, as well as ours, relies crucially on classical free boundaryregularity results due to Kinderlehrer and Nirenberg [18], and Caffarelli [6].

Singularities Almost Always Scatter: Regularity Results for Non-scattering Inhomogeneities