The local complex Calderón problem. Stability in a layered medium for a special type of anisotropic admittivity
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913814338863104 |
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| author | Foschiatti, Sonia Gaburro, Romina Sincich, Eva |
| author_facet | Foschiatti, Sonia Gaburro, Romina Sincich, Eva |
| contents | We deal with Calderón's problem in a layered anisotropic medium $Ω\subset\mathbb{R}^n$, $n\geq 3$, with complex anisotropic admittivity $σ=γA$, where $A$ is a known Lipschitz matrix-valued function. We assume that the layers of $Ω$ are fixed and known and that $γ$ is an unknown affine complex-valued function on each layer. We provide Hölder and Lipschitz stability estimates of $σ$ in terms of an ad hoc misfit functional as well as the more classical Dirichlet to Neumann map localised on some open portion $Σ$ of $\partialΩ$, respectively. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_03557 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The local complex Calderón problem. Stability in a layered medium for a special type of anisotropic admittivity Foschiatti, Sonia Gaburro, Romina Sincich, Eva Analysis of PDEs Mathematical Physics 35R30, 35J25, 35J47 We deal with Calderón's problem in a layered anisotropic medium $Ω\subset\mathbb{R}^n$, $n\geq 3$, with complex anisotropic admittivity $σ=γA$, where $A$ is a known Lipschitz matrix-valued function. We assume that the layers of $Ω$ are fixed and known and that $γ$ is an unknown affine complex-valued function on each layer. We provide Hölder and Lipschitz stability estimates of $σ$ in terms of an ad hoc misfit functional as well as the more classical Dirichlet to Neumann map localised on some open portion $Σ$ of $\partialΩ$, respectively. |
| title | The local complex Calderón problem. Stability in a layered medium for a special type of anisotropic admittivity |
| topic | Analysis of PDEs Mathematical Physics 35R30, 35J25, 35J47 |
| url | https://arxiv.org/abs/2408.03557 |