A global uniqueness theorem for an inverse boundary value problem
- J. Sylvester, G. Uhlmann
- Mathematics
- 1987
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…
RECOVERING A POTENTIAL FROM PARTIAL CAUCHY DATA
- A. Bukhgeǐm, G. Uhlmann
- Mathematics
- 5 January 2002
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.
Uniqueness in the inverse conductivity problem for nonsmooth conductivities in two dimensions
- Russell M. Brown, G. Uhlmann
- Mathematics
- 1997
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
Determining anisotropic real-analytic conductivities by boundary measurements
- John M. Lee, G. Uhlmann
- Mathematics
- 1 December 1989
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…
Thermoacoustic tomography with variable sound speed
- P. Stefanov, G. Uhlmann
- Mathematics
- 11 February 2009
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…
Limiting Carleman weights and anisotropic inverse problems
- David Dos Santos Ferreira, C. Kenig, M. Salo, G. Uhlmann
- Mathematics
- 25 March 2008
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
- R. Melrose, G. Uhlmann
- Mathematics
- 1 July 1979
The X-Ray Transform for a Generic Family of Curves and Weights
- Andrew Béla Frigyik, P. Stefanov, G. Uhlmann
- Mathematics
- 3 February 2007
Abstract
We study the weighted integral transform on a compact manifold with boundary over a smooth family of curves Γ. We prove generic injectivity and a stability estimate under the condition that…
Determining a Magnetic Schrödinger Operator from Partial Cauchy Data
- D. D. S. Ferreira, C. Kenig, J. Sjöstrand, G. Uhlmann
- Mathematics
- 19 January 2006
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…
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