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arXiv · 1604.02948

Uniqueness for the electrostatic inverse boundary value problem with piecewise constant anisotropic conductivities

Giovanni Alessandrini·Maarten V. de Hoop·Romina Gaburro
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Abstract

We discuss the inverse problem of determining the, possibly anisotropic, conductivity of a body $Ω\subset\mathbb{R}^{n}$ when the so-called Neumann-to-Dirichlet map is locally given on a non empty curved portion $Σ$ of the boundary $\partialΩ$. We prove that anisotropic conductivities that are \textit{a-priori} known to be piecewise constant matrices on a given partition of $Ω$ with curved interfaces can be uniquely determined in the interior from the knowledge of the local Neumann-to-Dirichlet map.

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Giovanni Alessandrini, Maarten V. de Hoop, Romina Gaburro. 2016-04-11. Uniqueness for the electrostatic inverse boundary value problem with piecewise constant anisotropic conductivities. https://doi.org/10.1088/1361-6420%2Faa982d

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