this paper) imply, via Sobolev embedding, that the conductivity is continuous. It is interesting to note that the only uniqueness results available for conductivities which are discontinuous are due to Kohn and Vogelius [9] who study conductivities which are piecewise analytic and V. Isakov [8] who considers a class of conductivities which are piecewise C

Abstract. Let Ω be a domain in R n whose boundary is C 1 if n ≥ 3 or C 1,β if n = 2. We consider a magnetic Schrödinger operator LW,q in Ω and show how to recover the boundary values of the tangential component of the vector potential W from the Dirichlet to Neumann map for LW,q. We also consider a steady state heat equation with convection term ∆+2W · ∇ and recover the boundary values of the convection term W from the Dirichlet to Neumann map. Our method is constructive and gives a stability result at the boundary. 1

this paper, we contribute nothing to the analysis of G # . The estimates used are from the paper of Sylvester and Uhlmannn [16]. It is possible that some improvement can be made here. We expect that one should be able to prove uniqueness for conductivities which have 3/2 derivatives in L with p > 2n/3. However, the straightforward generalization of the argument presented below would require that f # #G # f map functions which are compactly supported to functions which are locally in L with p and r satisfying 1/p 1/r = 1/n. Many such estimates fail, see [2] for further discussion

Abstract. We consider limiting Carleman weights for Dirac operators and prove corresponding Carleman estimates. In particular, we show that limiting Carleman weights for the Laplacian also serve as limiting weights for Dirac operators. As an application we consider the inverse problem of recovering a Lipschitz continuous magnetic field and electric potential from boundary measurements for the Pauli Dirac operator. 1.

Abstract. On a fixed smooth compact Riemann surface with boundary (M0, g), we show that for the Schrödinger operator ∆ + V with potential V ∈ C 1,α (M0) for some α> 0, the Dirichlet-to-Neumann map N|Γ measured on an open set Γ ⊂ ∂M0 determines uniquely the potential V. We also discuss briefly the corresponding consequences for potential scattering at 0 frequency on Riemann surfaces with asymptotically Euclidean or asymptotically hyperbolic ends. 1.

this paper, we contribute nothing to the analysis of G . The estimates used are from the paper of Sylvester and Uhlmannn [16]. It is possible that some improvement can be made here. We expect that one should be able to prove uniqueness for conductivities which have 3/2 derivatives in L with p > 2n=3. However, the straightforward generalization of the argument presented below would require that f ! rG f map functions which are compactly supported to functions which are locally in L with p and r satisfying 1=p 1=r = 1=n. Many such estimates fail, see [2] for further discussion

Abstract. We survey recent results on inverse boundary value problems for the magnetic Schrödinger equation. 1.