Alessandrini, G,de Hoop, MV,Gaburro, R

2017

December

Inverse Problems

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

Published

()

Calderon's problem electrical impedance tomography direct current (DC) method anisotropy ELECTRICAL-IMPEDANCE TOMOGRAPHY PARTIAL CAUCHY DATA TO-NEUMANN MAP ELLIPTIC-EQUATIONS CALDERON PROBLEM RIEMANNIAN-MANIFOLDS LIPSCHITZ STABILITY GLOBAL UNIQUENESS THEOREM WATER

33

We discuss the inverse problem of determining the, possibly anisotropic, conductivity of a body Omega subset of R-n when the so-called Neumann-to-Dirichlet map is locally given on a non-empty curved portion Sigma of the boundary partial derivative Omega. We prove that anisotropic conductivities that are 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.

10.1088/1361-6420/aa982d