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Using the translation method of Tartar, Murat, Lurie, and Cherkaev bounds arederived on the volume occupied by an inclusion in a three-dimensionalconducting body. They assume electrical impedance tomography measurements havebeen made for three sets of pairs of current flux and voltage measurementsaround the boundary. Additionally the conductivity of the inclusion andsurrounding medium are assumed to be known. If the boundary data (Dirichlet orNeumann) is special, i.e. such that the fields inside the body would be uniformwere the body homogeneous, then the bounds reduce to those of Milton and thuswhen the volume fraction is small to those of Capdeboscq and Vogelius.

Bounds on the volume fractions of two materials in a three dimensional body from boundary measurements by the translation method