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In this paper we improve an earlier result by Bukhgeim and Uhlmann [1], by showing that in dimension n ≥ 3, the knowledge of the Cauchy data for the Schrödinger equation measured on possibly very small subsets of the boundary determines uniquely the potential. We follow the general strategy of [1] but use a richer set of solutions to the Dirichlet problem.… (More)

- Leonid Pestov, Gunther Uhlmann
- 2008

We prove that knowing the lengths of geodesics joining points of the boundary of a two-dimensional, compact, simple Riemannian manifold with boundary, we can determine uniquely the Riemannian metric up to the natural obstruction.

Let R 2 be a bounded domain with Lipschitz boundary and let : ! R be a function which is measurable and bounded away from zero and innnity. We consider the divergence form elliptic operator

We construct anisotropic conductivities with the same Dirichlet-to-Neumann map as a homogeneous isotropic conductivity. These conductivities are singular close to a surface inside the body.

This paper analyzes the reconstruction of diffusion and absorption parameters in an elliptic equation from knowledge of internal data. In the application of photoacoustics, the internal data are the amount of thermal energy deposited by high frequency radiation propagating inside a domain of interest. These data are obtained by solving an inverse wave… (More)

In this paper we show, in dimension n ≥ 3, that knowledge of the Cauchy data for the Schrödinger equation in the presence of a magnetic potential, measured on possibly very small subsets of the boundary, determines uniquely the magnetic field and the electric potential. We follow the general strategy of [7] using a richer set of solutions to the Dirichlet… (More)

- Allan Greenleaf, Matti Lassas, Gunther Uhlmann
- Physiological measurement
- 2003

We construct anisotropic conductivities in dimension 3 that give rise to the same voltage and current measurements at the boundary of a body as a homogeneous isotropic conductivity. These conductivities are non-zero, but degenerate close to a surface inside the body.

Revised Abstract There has recently been considerable interest in the possibility, both theoretical and practical, of invisibility (or " cloaking ") from observation by electromagnetic (EM) waves. Here, we prove invisibility with respect to solutions of the Helmholtz and Maxwell's equations, for several constructions of cloaking devices. The basic idea, as… (More)

We prove that a potential q can be reconstructed from the Dirichlet-to-Neumann map for the Schrödinger operator −∆g + q in a fixed admissible 3-dimensional Riemannian manifold (M, g). We also show that an admissible metric g in a fixed conformal class can be constructed from the Dirichlet-to-Neumann map for ∆g. This is a constructive version of earlier… (More)