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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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