2011/12/08 by Amir Moradifam, Adrian Nachman, Moradifam, Amir +3
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Electrical and Bioimpedance Tomography #FOS: Mathematics #Numerical methods in inverse problems #Photoacoustic and Ultrasonic Imaging #math.AP
paper · pdf · doi:10.48550/arxiv.1112.2002
openalex publication_date 2011/12/08 · arxiv created 2011/12/09 · arxiv updated 2011/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the problem of recovering an isotropic conductivity outside some perfectly conducting or insulating inclusions from the interior measurement of the magnitude of one current density field |J|. We prove that the conductivity outside the inclusions, and the shape and position of the perfectly conducting and insulating inclusions are uniquely determined (except in an exceptional case) by the magnitude of the current generated by imposing a given boundary voltage. We have found an extension of the notion of admissibility to the case of possible presence of perfectly conducting and insulating inclusions. This also makes it possible to extend the results on uniqueness of the minimizers of the least gradient problem F(u)=∫Ωa|∇ u| with u|∂ Ω=f to cases where u has flat regions (is constant on open sets).