The inverse conductivity problem with one measurement: uniqueness for convex polyhedra

Let Ω Ω denote a smooth domain in R n {R^n} containing the closure of a convex polyhedron D . Set χ D {χ _D} equal to the characteristic function of D . We find a flux g so that if u is the nonconstant solution of div ( ( 1 + χ D ) ∇ u ) = 0 div\;((1 + {χ _D})∇ u) = 0 in Ω Ω with ∂ u ∂ n = g {{∂ u}}{{∂ n}} = g on ∂ Ω ∂ Ω , then D is uniquely determined by the Cauchy data g and f ≡ u / ∂ Ω f ≡ u/∂ Ω .