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arXiv · 2507.19410

Reconstruction in the Calder\'on problem on a fixed partition from finite and partial boundary data

Henrik Garde
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Abstract

This short note modifies a reconstruction method by the author (Comm. PDE, 45(9):1118-1133, 2020), for reconstructing piecewise constant conductivities in the Calder\'on problem (electrical impedance tomography). In the former paper, a layering assumption and the local Neumann-to-Dirichlet map were needed since the piecewise constant partition also was assumed unknown. Here I show how to modify the method in case the partition is known, for general piecewise constant conductivities and only a finite number of partial boundary measurements. Moreover, no lower/upper bounds on the unknown conductivity are needed.

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Henrik Garde. 2025-07-25. Reconstruction in the Calder\'on problem on a fixed partition from finite and partial boundary data. https://doi.org/10.1016/j.aml.2025.109841

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