Comptes Rendus
Partial differential equations
Extending representation formulas for boundary voltage perturbations of low volume fraction to very contrasted conductivity inhomogeneities
Comptes Rendus. Mathématique, Volume 360 (2022), pp. 127-150.

Imposing either Dirichlet or Neumann boundary conditions on the boundary of a smooth bounded domain Ω, we study the perturbation incurred by the voltage potential when the conductivity is modified in a set of small measure. We consider (γ n ) n , a sequence of perturbed conductivity matrices differing from a smooth γ 0 background conductivity matrix on a measurable set well within the domain, and we assume (γ n -γ 0 )γ n -1 (γ n -γ 0 )0 in L 1 (Ω). Adapting the limit measure, we show that the general representation formula introduced for bounded contrasts in a previous work from 2003 can be extended to unbounded sequences of matrix valued conductivities.

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DOI: 10.5802/crmath.273
Yves Capdeboscq 1; Shaun Chen Yang Ong 2

1 Université de Paris and Sorbonne Université, CNRS, Laboratoire Jacques-Louis Lions (LJLL), F-75006 Paris, France
2 Mathematical Institute, University of Oxford, OX2 6GG, UK
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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     title = {Extending representation formulas for boundary voltage perturbations of low volume fraction to very contrasted conductivity inhomogeneities},
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Yves Capdeboscq; Shaun Chen Yang Ong. Extending representation formulas for boundary voltage perturbations of low volume fraction to very contrasted conductivity inhomogeneities. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 127-150. doi : 10.5802/crmath.273. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.273/

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