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The determination of a discontinuity in a conductivity from a single boundary measurement. (English) Zbl 0894.35126

Summary: We consider the determination of the interior domain \(D\subset \Omega\), 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 \(a= 1+\chi_D\) in \(\text{div}(a\nabla u)= 0\) from boundary data consisting of Cauchy data on the boundary of the exterior domain \(\Omega\). 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.

MSC:

35R30 Inverse problems for PDEs
35J25 Boundary value problems for second-order elliptic equations
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