G. Uhlmann

Publications359
h-index65
Citations14,882
Highly Influential Citations970
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A global uniqueness theorem for an inverse boundary value problem
In this paper, we show that the single smooth coefficient of the elliptic operator LY = v yv can be determined from knowledge of its Dirichlet integrals for arbitrary boundary values on a fixed…
Uniqueness in the inverse conductivity problem for nonsmooth conductivities in two dimensions
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
RECOVERING A POTENTIAL FROM PARTIAL CAUCHY DATA
ABSTRACT In this paper we prove in dimension n ⪆ 3 that knowledge of the Cauchy data for the Schrödinger equation measured on particular subsets of the boundary determines uniquely the potential.
Thermoacoustic tomography with variable sound speed
We study the mathematical model of thermoacoustic tomography in media with a variable speed for a fixed time interval [0, T] so that all signals issued from the domain leave it after time T. In the…
Determining anisotropic real-analytic conductivities by boundary measurements
If an electrical potential is applied to the surface of a solid body, the current flux across the surface depends on the conductivity in the interior of the body. We want to consider the inverse…
Limiting Carleman weights and anisotropic inverse problems
In this article we consider the anisotropic Calderón problem and related inverse problems. The approach is based on limiting Carleman weights, introduced in Kenig et al. (Ann. Math. 165:567–591,…
Lagrangian Intersection and the Cauchy Problem
The Calderón problem with partial data
In this paper we improve an earlier result by Bukhgeim and Uhlmann, by showing that in dimension larger than or equal to three, the knowledge of the Cauchy data for the Schr\"odinger equation…
Determining a Magnetic Schrödinger Operator from Partial Cauchy Data
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…
Inverse Diffusion Theory of Photoacoustics
This paper analyzes the reconstruction of diffusion and absorption parameters in an elliptic equation from knowledge of internal data. In the application of photo-acoustics, the internal data are the…
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