Determining conductivity and embedded obstacles from partial boundary measurements

Abstract

In this paper, we consider an inverse conductivity problem on a bounded domain $\Omega \subset {\mathbb{R}}^n$, $n\ge 2$, also known as Electrical Impedance Tomography (EIT), for the case where unknown impenetrable obstacles are embedded into $\Omega$. We show that a piecewise-constant conductivity function and embedded obstacles can be simultaneously recovered in terms of the local Dirichlet-to-Neumann map defined on an arbitrary small open subset of the boundary of the domain $\Omega$. The method depends on the well-posedness of a coupled PDE-system constructed for the conductivity equations in the $H^1$-space and some elementary a priori estimates for Harmonic functions.

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