Uniqueness results for inverse Robin problems with bounded coefficient

In this paper we address the uniqueness issue in the classical Robin inverse problem on a Lipschitz domain Ω⊂Rn, with L∞ Robin coefficient, L2 Neumann data and conductivity of class W1,r(Ω), r>n. We show that uniqueness of the Robin coefficient on a subpart of the boundary, given Cauchy data on the complementary part, does hold in dimension n=2 but needs not hold in higher dimension. We also raise on open issue on harmonic gradients which is of interest in this context.