On a novel UCP result and its application to inverse conductive scattering

In this paper, we derive a novel Unique Continuation Principle (UCP) for a system of second-order elliptic PDEs system and apply it to investigate inverse problems in conductive scattering. The UCP relaxes the typical assumptions imposed on the domain or boundary with certain interior transmission conditions. This is motivated by the study of the associated inverse scattering problem and enables us to establish several novel unique identifiability results for the determination of generalized conductive scatterers using a single far-field pattern, significantly extending the results in [12,18]. A key technical advancement in our work is the combination of Complex Geometric Optics (CGO) techniques from [12,18] with the Fourier expansion method to microlocally analyze corner singularities and their implications for inverse problems. We believe that the methods developed can have broader applications in other contexts.