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arXiv · 2107.04879

Stability for the Calderón's problem for a class of anisotropic conductivities via an ad-hoc misfit functional

Sonia Foschiatti·Romina Gaburro·Eva Sincich
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Abstract

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.

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Sonia Foschiatti, Romina Gaburro, Eva Sincich. 2022-07-15. Stability for the Calderón's problem for a class of anisotropic conductivities via an ad-hoc misfit functional. https://doi.org/10.1088/1361-6420%2Fac349c

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