Uniqueness of the inverse conductivity problem once-differentiable complex conductivities in three dimensions

Ivan Pombo

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arXiv · 2301.08663

Uniqueness of the inverse conductivity problem once-differentiable complex conductivities in three dimensions

Ivan Pombo

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Abstract

We prove uniqueness of the inverse conductivity problem in three dimensions for complex conductivities in $W^{1,\infty}$. We apply quaternionic analysis to transform the inverse problem into an inverse Dirac scattering problem, as established in two dimensions by Brown and Uhlmann. This is a novel methodology that allows to extend the uniqueness result from once-differentiable real conductivities to complex ones.

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Ivan Pombo. 2023-01-20. Uniqueness of the inverse conductivity problem once-differentiable complex conductivities in three dimensions. https://arxiv.org/abs/2301.08663

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