Reconstruction of non-self-adjoint anisotropic and complex inclusions in the Calderón problem
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910194619908096 |
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| author | Garde, Henrik Johansson, David Zacharopoulos, Thanasis |
| author_facet | Garde, Henrik Johansson, David Zacharopoulos, Thanasis |
| contents | We generalize recent results on the monotonicity method, for inclusion detection in the partial data anisotropic Calderón problem, to very general non-self-adjoint perturbations. This involves a forward model that accounts for both the anisotropic real conductivity and the anisotropic permittivity, and the results hold in any spatial dimension $d \geq 2$. We assume that the inclusion boundaries can be reached from the domain boundary via a set on which the background conductivity is self-adjoint, and that a definiteness condition holds near the inclusion boundaries. Away from the inclusion boundaries we allow general $L^\infty$ non-self-adjoint perturbations. We only require unique continuation based on the self-adjoint part of the background conductivity, thus making the methods compatible with generic unique continuation results. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_05021 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Reconstruction of non-self-adjoint anisotropic and complex inclusions in the Calderón problem Garde, Henrik Johansson, David Zacharopoulos, Thanasis Analysis of PDEs 35R30, 35R05, 47H05 We generalize recent results on the monotonicity method, for inclusion detection in the partial data anisotropic Calderón problem, to very general non-self-adjoint perturbations. This involves a forward model that accounts for both the anisotropic real conductivity and the anisotropic permittivity, and the results hold in any spatial dimension $d \geq 2$. We assume that the inclusion boundaries can be reached from the domain boundary via a set on which the background conductivity is self-adjoint, and that a definiteness condition holds near the inclusion boundaries. Away from the inclusion boundaries we allow general $L^\infty$ non-self-adjoint perturbations. We only require unique continuation based on the self-adjoint part of the background conductivity, thus making the methods compatible with generic unique continuation results. |
| title | Reconstruction of non-self-adjoint anisotropic and complex inclusions in the Calderón problem |
| topic | Analysis of PDEs 35R30, 35R05, 47H05 |
| url | https://arxiv.org/abs/2605.05021 |