Reconstruction of Planar Conductivities in Subdomains from Incomplete Data

We consider the problem of recovering a sufficiently smooth isotropic conductivity from interior knowledge of the magnitude of the current density field |J | generated by an imposed voltage potential f on the boundary. In any dimension n ≥ 2, we show that equipotential sets are global area minimizers in the conformal metric determined by |J |. In two… (More)