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

TL;DR

This paper proves that piecewise constant anisotropic conductivities within a body can be uniquely identified from local boundary measurements, advancing the understanding of inverse boundary value problems in mathematical physics.

Contribution

It establishes the uniqueness of determining piecewise constant anisotropic conductivities from local boundary data, a novel result in inverse boundary value problems.

Findings

Uniqueness of anisotropic conductivities with curved interfaces

Determination from local Neumann-to-Dirichlet map

Applicable to piecewise constant matrices

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.