Uniqueness and stability in an inverse problem for the Schr dinger equation

We study the Schrödinger equation i y ′ + Δ y + qy = 0 in Ω × (0, T ) with Dirichlet boundary data y | ∂Ω×(0, T ) and initial condition y | Ω×{0} and we consider the inverse problem of determining the potential q ( x ), x ∊ Ω when ∂ y /∂ν| Γ 0 ×(0, T ) is given. Here Ω is an open-bounded domain of ℝ N , Γ 0 is an open subset of ∂Ω satisfying a suitable geometrical condition and T > 0. More precisely, from a global Carleman estimate we prove a stability inequality between | p − q | and | ∂ y ( q )/∂ν − ∂ y ( p )/∂ν| with appropriate norms.