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 Omega of conductivity sigma = 1, an unknown inclusion D, whose conductivity is sigma = k not equal 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.