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arXiv · 2408.03557

The local complex Calderón problem. Stability in a layered medium for a special type of anisotropic admittivity

Sonia Foschiatti·Romina Gaburro·Eva Sincich
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Abstract

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.

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Sonia Foschiatti, Romina Gaburro, Eva Sincich. 2025-05-01. The local complex Calderón problem. Stability in a layered medium for a special type of anisotropic admittivity. https://arxiv.org/abs/2408.03557

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