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Zbl 0625.35078
Sylvester, John; Uhlmann, Gunther
A global uniqueness theorem for an inverse boundary value problem.
(English)
[J] Ann. Math. (2) 125, 153-169 (1987). ISSN 0003-486X; ISSN 1939-0980/e

The authors prove that the single smooth coefficient, $\gamma$, of the elliptic operator $L\sb{\gamma}=\nabla \cdot \gamma \nabla$ in a bounded region $\Omega \le {\bbfR}\sp n$ (n$\ge 3)$ can be recovered from the map which sends the boundary values of a $\gamma$-harmonic function u $(L\sb{\gamma}u=0$ in $\Omega)$ to the boundary values of its conormal derivative $\gamma$ ($\partial u/\partial \nu)$. This shows that the isotropic conductivity of a body can, in principal, be recovered from voltage to current measurement at the boundary.
MSC 2000:
*35R30 Inverse problems for PDE
35J05 Laplace equation, etc.
31A25 Boundary value and inverse problems (two-dim.potential theory)
31A05 Harmonic functions, etc. (two-dimensional)

Keywords: global uniqueness; Dirichlet to Neumann map; inverse boundary value problem; smooth coefficient; harmonic function; isotropic conductivity; body; recovered from voltage

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