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Identification of small inhomogeneities of extreme conductivity by boundary measurements: A theorem on continuous dependence. (English) Zbl 0684.35087
The authors consider the inverse problem to determine perturbations of the coefficient \(\gamma\) (x) in the differential equation \(\nabla \cdot (\gamma \nabla u)=0\) in \(\Omega <{\mathbb{R}}^ n\), \(n\geq 2\), from measurements of u and \(\gamma\) (\(\partial u/\partial \nu)\) on the boundary \(\partial \Omega\). They treat the cases where the perturbed coefficients are either infinite or zero on a finite (but unknown) number of small (order \(\epsilon)\) subregions of \(\Omega\). In the first part they prove an asymptotic formula of the field \(u_{\epsilon}\) with respect to \(\epsilon\). In the second part this result is used to prove a Lipschitz-continuous dependence estimate of the function which maps - for fixed Neumann data - the Dirichlet data onto the parameters describing \(\gamma\).
Reviewer: A.Kirsch

MSC:
35R30 Inverse problems for PDEs
78A30 Electro- and magnetostatics
35J25 Boundary value problems for second-order elliptic equations
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