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

Abstract:

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