Reconstruction in the Calderón problem on a fixed partition from finite and partial boundary data
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908694621454336 |
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| author | Garde, Henrik |
| author_facet | Garde, Henrik |
| contents | This short note modifies a reconstruction method by the author (Comm. PDE, 45(9):1118-1133, 2020), for reconstructing piecewise constant conductivities in the Calderón 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_19410 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reconstruction in the Calderón problem on a fixed partition from finite and partial boundary data Garde, Henrik Analysis of PDEs Numerical Analysis 35R30, 35Q60, 35R05, 47H05 This short note modifies a reconstruction method by the author (Comm. PDE, 45(9):1118-1133, 2020), for reconstructing piecewise constant conductivities in the Calderón 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. |
| title | Reconstruction in the Calderón problem on a fixed partition from finite and partial boundary data |
| topic | Analysis of PDEs Numerical Analysis 35R30, 35Q60, 35R05, 47H05 |
| url | https://arxiv.org/abs/2507.19410 |