Split Corners in Scattering and Inverse Scattering

Abstract

We study scattering and inverse scattering generated by sources and penetrable media with corner singularities. We introduce the notion of split corners, a local model that unifies geometric singularities and coefficient discontinuities arising in source and medium scattering. Within this framework, we establish scattering and inverse scattering results that extend the classical theory to split corners, allowing the source or medium contrast to approach different limiting values in distinct sectors meeting at the corner tip. For source scattering, we prove that every admissible two-split corner necessarily radiates in a general bounded inhomogeneous background, thereby generalizing the classical corner radiation principle to configurations involving both geometric corners and jump discontinuities. For penetrable media, we establish analogous results together with explicit compatibility conditions for incident waves of arbitrary vanishing order. As consequences, we obtain several uniqueness results in inverse source and inverse medium scattering, including recovery of polygonal convex hulls from a single far-field measurement.