Inverse problem for a planar conductivity inclusion
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- June 2022
- DOI:
- 10.48550/arXiv.2206.05593
- arXiv:
- arXiv:2206.05593
- Bibcode:
- 2022arXiv220605593C
- Keywords:
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- Mathematics - Analysis of PDEs;
- 30C35;
- 35J05;
- 45P05
- E-Print:
- 29 pages, 6 figures