  A finite element code for heat conduction, together with an adjoint solver
and a suite of optimization tools was applied for the solution of Calderon's
problem. One of the questions whose answer was sought was whether the solution
to these problems is unique and obtainable. The results to date show that while
the optimization procedure is able to obtain spatial distributions of the
conductivity $k$ that reduce the cost function significantly, the resulting
conductivity $k$ is still significantly different from the target distribution
sought. While the normal fluxes recovered are very close to the prescribed
ones, the tangential fluxes can differ considerably.
