The Inverse Conductivity Problem with One Measurement: Bounds on the Size of the Unknown Object

Abstract

We consider the problem of determining, within an electrically conducting body $\Omega$ of conductivity $\sigma\equiv 1$, an unknown inclusion D, whose conductivity is $\sigma\equiv k\neq 1$, when one pair of current density and voltage measurements {}from the exterior of $\Omega$ is available. We prove upper and lower bounds on the size of the unknown inclusion D. We also consider the case of nonuniform and nonisotropic conductivities in $\Omega$ and in D.