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A global uniqueness theorem for an inverse boundary value problem. (English) Zbl 0625.35078
The authors prove that the single smooth coefficient, \(\gamma\), of the elliptic operator \(L_{\gamma}=\nabla \cdot \gamma \nabla\) in a bounded region \(\Omega \leq {\mathbb{R}}^ n\) (n\(\geq 3)\) can be recovered from the map which sends the boundary values of a \(\gamma\)-harmonic function u \((L_{\gamma}u=0\) 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:
35R30 Inverse problems for PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
31A25 Boundary value and inverse problems for harmonic functions in two dimensions
31A05 Harmonic, subharmonic, superharmonic functions in two dimensions
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