Uniqueness for the electrostatic inverse boundary value problem with piecewise constant anisotropic conductivities. (22nd November 2017)

• Record Type: Journal Article
• Authors: Alessandrini, Giovanni; de Hoop, Maarten V; Gaburro, Romina
• Is Part Of: Inverse problems. Volume 33:Number 12(2017:Dec.)
• Publication Date: 2017-11-22
• Subjects: Calderòn's problem -- electrical impedance tomography -- direct current (DC) method -- anisotropy; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aa982d
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We discuss the inverse problem of determining the, possibly anisotropic, conductivity of a body Ω ⊂ R n when the so-called Neumann-to-Dirichlet map is locally given on a non-empty curved portion Σ of the boundary ∂ Ω . We prove that anisotropic conductivities that are 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.