The determination of a discontinuity in a conductivity from a single boundary measurement
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We consider the determination of the interior domain D ⊂ Ω where D is characterized by a different conductivity from the surrounding medium. This amounts to solving the inverse problem of recovering the piecewise constant conductivity a = 1 + χD in div(a ∇u) = 0 from boundary data consisting of Cauchy data on the boundary of the exterior domain Ω. We will compute the derivative of the map from the domain D to this data and use this to obtain both qualitative and quantitative measures of the solution of the inverse problem.
author list (cited authors)
Hettlich, F., & Rundell, W.