Erratum: An Inverse Backscatter Problem for Electric Impedance Tomography

In the paper [1] we have claimed (in the concluding remarks) that the same arguments that we have used in the rest of the paper for insulating cavities can also be applied to establish that two (simply connected) perfectly conducting inclusions with the same backscatter data of impedance tomography are necessarily the same. Unfortunately, while our uniqueness result for insulating cavities is absolutely correct, the corresponding statement on perfect conductors fails to be true, and we will provide a counterexample below. A correct statement is as follows. (Throughout, we say that a perfect conductor is supported in the closure of a domain Ω if the homogeneous Neumann condition on Γ = ∂Ω in the forward problem associated with the backscatter data, i.e., [1, (2.16)], is replaced by a homogeneous Dirichlet condition, and the normalizing condition on T = ∂D is deleted.) Theorem 1. Assume that Ω is a simply connected domain with C-boundary, and that a perfect conductor is supported in Ω ⊂ D, where D is the unit disk. Let Φ be a conformal map that takes D \ Ω onto a concentric annulus {x ∈ D : R < |x| < 1}, and define