On Calderón's inverse inclusion problem with smooth shapes by a single partial boundary measurement. (15th April 2021)

• Record Type: Journal Article
• Authors: Liu, Hongyu; Tsou, Chun-Hsiang; Yang, Wei
• Is Part Of: Inverse problems. Volume 37:Number 5(2021)
• Publication Date: 2021-04-15
• Subjects: Calderon's inverse problem -- electric impedance tomography -- conductive inclusion -- smooth shape -- high curvature -- single partial boundary measurement; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/abefeb
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We consider Calderón's inverse inclusion problem of recovering the shape of an anomalous inhomogeneity embedded in a homogeneous conductivity by the associated electric boundary measurements. It is a longstanding problem whether one can establish the unique recovery result by a single boundary measurement. In several existing works, it is shown that corner singularities can help to resolve the problem within polygonal or polyhedral shapes. In this paper, under a generic technical condition, we show that the corner singularity can be relaxed to be a certain high-curvature condition and derive novel unique recovery results within smooth shapes.