Identification of small inhomogeneities of extreme conductivity by boundary measurements: A theorem on continuous dependence
type: Item
instance of: scholarly article
title: Identification of small inhomogeneities of extreme conductivity by boundary measurements: A theorem on continuous dependence
zbMATH Open document ID: 0684.35087
DOI: 10.1007/BF00281494
author: A. Friedman
author: Michael S. Vogelius
published in: Archive for Rational Mechanics and Analysis
publication date: 1989-01-01T00:00:00Z
review text: 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 \(\gamma\).
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 78A30
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 4120698
zbMATH Keywords: continuous dependence
zbMATH Keywords: perturbations of the coefficient
reviewed by: Andreas Kirsch
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4120698