Singularities almost always scatter: Regularity results for non‐scattering inhomogeneities
Fioralba Cakoni, Michael Vogelius
Abstract
Abstract In this paper we examine necessary conditions for an inhomogeneity to be non‐scattering, or equivalently, by negation, sufficient conditions for it to be scattering. These conditions are formulated in terms of the regularity of the boundary of the inhomogeneity. We examine broad classes of incident waves in both two and three dimensions. Our analysis is greatly influenced by the analysis carried out by Williams in order to establish that a domain, which does not possess the Pompeiu Property, has a real analytic boundary. That analysis, as well as ours, relies crucially on classical free boundary regularity results due to Kinderlehrer and Nirenberg, and Caffarelli.
Topics & Concepts
MathematicsGravitational singularityBoundary (topology)ScatteringDomain (mathematical analysis)Boundary value problemProperty (philosophy)Mathematical analysisOpticsPhysicsPhilosophyEpistemologyNumerical methods in inverse problemsAdvanced Mathematical Modeling in EngineeringMicrowave Imaging and Scattering Analysis