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Abstract
We consider the reconstruction of the support of an unknown perturbation to a known conductivity coefficient in Calderón’s problem. In a previous result by the authors on monotonicitybased reconstruction, the perturbed coefficient is allowed to simultaneously take the values 0 and ∞ in some parts of the domain and values bounded away from 0 and ∞ elsewhere. We generalise this result by allowing the unknown coefficient to be the restriction of an A _{2}Muckenhoupt weight in parts of the domain, thereby including singular and degenerate behaviour in the governing equation. In particular, the coefficient may tend to 0 and ∞ in a controlled manner, which goes beyond the standard setting of Calderón’s problem. Our main result constructively characterises the outer shape of the support of such a general perturbation, based on a local NeumanntoDirichlet map defined on an open subset of the domain boundary.
Original language  English 

Pages (fromto)  12191227 
Number of pages  9 
Journal  Inverse Problems and Imaging 
Volume  16 
Issue number  5 
Early online date  Apr 2022 
DOIs  
Publication status  Published  2022 
MoE publication type  A1 Journal articlerefereed 
Keywords
 Calderon's problem
 electrical impedance tomography
 monotonicity method
 inclusion detection
 degenerate elliptic problem
 singular elliptic problem
 SHAPERECONSTRUCTION
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Dive into the research topics of 'Reconstruction of singular and degenerate inclusions in Calderón's problem'. Together they form a unique fingerprint.Projects
 1 Finished

: Centre of Excellence of Inverse Modelling and Imaging
Hyvönen, N., Vavilov, A., Autio, A., Candiani, V., Perkkiö, L., Puska, J., Hirvi, P. & Kuutela, T.
01/05/2020 → 31/12/2022
Project: Academy of Finland: Other research funding