Recovery of L p-potential in the plane

An inverse problem for the two-dimensional Schrödinger equation with Lp-potential, p>1, is considered. Using the dbar-method, the potential is recovered from the Dirichlet-to-Neumann map on the boundary of a domain containing the support of the potential. We do not assume that the potential is small or that the Faddeev scattering problem does not have exceptional points. The paper contains a new estimate on the Faddeev Green function that immediately implies the absence of exceptional points near the origin and infinity when the potential v belongs to Lp