ON A NOVEL UNIQUE CONTINUATION PRINCIPLE 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 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 [X. Cao, H. Diao, and H. Liu, CSIAM Trans. Appl. Math., 1 (2020), pp. 740--765; H. Diao, X. Cao, and H. Liu, Comm. Partial Differential Equations, 46 (2021), pp. 630--679]. A key technical advancement in our work is the combination of complex geometric optics techniques from those cited works 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. © 2025 Society for Industrial and Applied Mathematics.