Stability for the Calderón's problem for a class of anisotropic conductivities via an ad-hoc misfit functional
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| Format: | Preprint |
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2021
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| _version_ | 1866911979797479424 |
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| author | Foschiatti, Sonia Gaburro, Romina Sincich, Eva |
| author_facet | Foschiatti, Sonia Gaburro, Romina Sincich, Eva |
| contents | We address the stability issue in Calderón's problem for a special class of anisotropic conductivities of the form $σ=γA$ in a Lipschitz domain $Ω\subset\mathbb{R}^n$, $n\geq 3$, where $A$ is a known Lipschitz continuous matrix-valued function and $γ$ is the unknown piecewise affine scalar function on a given partition of $Ω$. We define an ad-hoc misfit functional encoding our data and establish stability estimates for this class of anisotropic conductivity in terms of both the misfit functional and the more commonly used local Dirichlet-to-Neumann map. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2107_04879 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Stability for the Calderón's problem for a class of anisotropic conductivities via an ad-hoc misfit functional Foschiatti, Sonia Gaburro, Romina Sincich, Eva Analysis of PDEs 35R30 We address the stability issue in Calderón's problem for a special class of anisotropic conductivities of the form $σ=γA$ in a Lipschitz domain $Ω\subset\mathbb{R}^n$, $n\geq 3$, where $A$ is a known Lipschitz continuous matrix-valued function and $γ$ is the unknown piecewise affine scalar function on a given partition of $Ω$. We define an ad-hoc misfit functional encoding our data and establish stability estimates for this class of anisotropic conductivity in terms of both the misfit functional and the more commonly used local Dirichlet-to-Neumann map. |
| title | Stability for the Calderón's problem for a class of anisotropic conductivities via an ad-hoc misfit functional |
| topic | Analysis of PDEs 35R30 |
| url | https://arxiv.org/abs/2107.04879 |