TY - JOUR
T1 - Singularities almost always scatter
T2 - Regularity results for non-scattering inhomogeneities
AU - Cakoni, Fioralba
AU - Vogelius, Michael S.
N1 - Publisher Copyright:
© 2023 Wiley Periodicals LLC.
PY - 2023/12
Y1 - 2023/12
N2 - 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.
AB - 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.
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U2 - 10.1002/cpa.22117
DO - 10.1002/cpa.22117
M3 - Article
AN - SCOPUS:85165247141
SN - 0010-3640
VL - 76
SP - 4022
EP - 4047
JO - Communications on Pure and Applied Mathematics
JF - Communications on Pure and Applied Mathematics
IS - 12
ER -