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

We consider the problem of determining, within an electrically conducting body Ω of conductivity σ≡ 1, an unknown inclusion D, whose conductivity is σ≡ k≠ 1, when one pair of current density and voltage measurements {}from the exterior of Ω 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 Ω and in D.