On the inverse problem for three-dimensional potential scattering

AbstractWe consider a linear perturbation for the wave equation □u = 0 in Ω = E3 by “repulsive” smooth potentials q(y) that are small at infinity and suitably small (in magnitude). We use a time-dependent approach to prove that the scattering operator S(q) determines uniquenes uniquely the scatterer q (at least in this class). Energy inequalities will play a central role in our discussion