We prove uniqueness for the Calderón problem with Lipschitz conductivities in higher dimensions. Combined with the recent work of Haberman, who treated the three-and four-dimensional cases, this confirms a conjecture of Uhlmann. Our proof builds on the work of Sylvester and Uhlmann, Brown, and Haberman and Tataru who proved uniqueness for C 1 -conductivities and Lipschitz conductivities sufficiently close to the identity.

We prove a uniqueness theorem for an inverse boundary value problem for the Maxwell system with boundary data assumed known only in part of the boundary. We assume that the inaccessible part of the boundary is either part of a plane, or part of a sphere. This work generalizes the results obtained by Isakov [I] for the Schrödinger equation to Maxwell equations.

In this paper we consider an inverse problem for the n-dimensional random Schrödinger equation (∆ − q + k 2 )u = 0. We study the scattering of plane waves in the presence of a potential q which is assumed to be a Gaussian random function such that its covariance is described by a pseudodifferential operator. Our main result is as follows: given the backscattered far field, obtained from a single realization of the random potential q, we uniquely determine the principal symbol of the covariance operator of q. Especially, for n = 3 this result is obtained for the full non-linear inverse backscattering problem. Finally, we present a physical scaling regime where the method is of practical importance. 35 4.4. Non-zero-mean potentials 37 Appendix A. Scaling regimes 40 A.1. Two-scale model of a non-smooth scatterer 40 A.2. Inverse scattering with the two-scale model 43 A.3. Effects from the higher order scattering 44 Appendix B. Random variables with Gaussian probability laws 47 References

In this paper we prove a stable determination of the coefficients of the time-harmonic Maxwell equations from local boundary data. The argument -due to Isakov-requires some restrictions on the domain.