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Extending representation formulas for boundary voltage perturbations of low volume fraction to very contrasted conductivity inhomogeneities
Capdeboscq, Yves1   ; Ong, Shaun Chen Yang2
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
Comptes Rendus. Mathématique, Tome 360 (2022) no. G2, pp. 127-150.

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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 (γn)n∈ℕ, a sequence of perturbed conductivity matrices differing from a smooth γ0 background conductivity matrix on a measurable set well within the domain, and we assume (γn-γ0)γn-1(γn-γ0)→0 in L1(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

Capdeboscq, Yves 1 ; Ong, Shaun Chen Yang 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
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Capdeboscq, Yves; Ong, Shaun Chen Yang. Extending representation formulas for boundary voltage perturbations of low volume fraction to very contrasted conductivity inhomogeneities. Comptes Rendus. Mathématique, Tome 360 (2022) no. G2, pp. 127-150. doi : 10.5802/crmath.273. https://geodesic-test.mathdoc.fr/articles/10.5802/crmath.273/

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