Inverse problem for a planar conductivity inclusion

2022/06/11 by Doosung Choi, Choi, Doosung, Johan Helsing +5
Engineering · Mathematics · Physics and Astronomy · #30C35 #35J05 #45P05 #Analysis of PDEs (math.AP) #Composite Material Mechanics #Electromagnetic Scattering and Analysis #FOS: Mathematics #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2206.05593

openalex publication_date 2022/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper concerns the inverse problem of determining a planar conductivity inclusion. Our aim is to analytically recover from the generalized polarization tensors (GPTs), which can be obtained from exterior measurements, a homogeneous inclusion with arbitrary constant conductivity. The primary outcome of recovering a homogeneous inclusion is an inversion formula in terms of the GPTs for conformal mapping coefficients associated with the inclusion. To prove the formula, we establish matrix factorizations for the GPTs.

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