A uniqueness theorem for an inverse boundary value problem in two dimensions ✩

We consider the inverse problem to determine the potential q entering the Schrödinger equation Δu − qu = 0 in a bounded smooth domain in R2 in terms of the boundary measurements (Dirichlet-to-Neumann map). When n = 3, the uniqueness for the inverse problem was well established. In this paper we prove the uniqueness in two dimensions under the assumption that the Lp (p > 2) norm of q is small. This result improves a uniqueness result of Sylvester–Uhlmann under the assumption that the W1,∞ norm of q is small.  2002 Elsevier Science (USA). All rights reserved.