We consider the problem of the determination of the potential from the Dirichlet to Neumann map of the Schrödinger operator. We show that this problem is severely ill posed. The results extend to the electrical impedance tomography. They show that the logarithmic stability results of Alessandrini are optimal.

with C−1 ≤ ρ ≤ C, C > 1. When n = 3 it describes the evolution of temperature u in a medium where the thermal conductivity is constant and the heat capacity is ρ. It also applies to diffusion in porous rocks, where ρ is the specific storage, if the hydraulic conductivity is constant. We consider the problem of the determination of ρ in Ω from boundary… (More)