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

Abstract

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

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Cited by in corpus (13)

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• Calderón's Inverse Problem with a Finite Number of Measurements
• On Calderón's inverse inclusion problem with smooth shapes by a single partial boundary measurement
• Inverse problems on low-dimensional manifolds
• Levenberg-Marquardt method with Singular Scaling and applications
• Calderón's Inverse Problem with a Finite Number of Measurements II: Independent Data
• Uniqueness in the inverse boundary value problem for piecewise homogeneous anisotropic elasticity
• Unique recovery of piecewise analytic density and stiffness tensor from the elastic-wave Dirichlet-to-Neumann map
• Stable determination of polygonal inclusions in Calderón's problem by a single partial boundary measurement
• CGO-Faddeev approach for Complex Conductivities with Regular Jumps
• Local recovery of a piecewise constant anisotropic conductivity in EIT on domains with exposed corners
• Series reversion in Calderón's problem
• Stability for the Calderón's problem for a class of anisotropic conductivities via an ad-hoc misfit functional