Extending representation formulas for boundary voltage perturbations of low volume fraction to very contrasted conductivity inhomogeneities - Sorbonne Université
Article Dans Une Revue Comptes Rendus. Mathématique Année : 2022

Extending representation formulas for boundary voltage perturbations of low volume fraction to very contrasted conductivity inhomogeneities

Yves Capdeboscq
Shaun Chen Yang Ong
  • Fonction : Auteur
  • PersonId : 1093799

Résumé

Imposing either Dirichlet or Neumann boundary conditions on the boundary of a smooth bounded domain $\Omega$, we study the perturbation incurred by the voltage potential when the conductivity is modified in a set of small measure. We consider $\left(\gamma_{n}\right)_{n\in\mathbb{N}}$, a sequence of perturbed conductivity matrices differing from a smooth $\gamma_{0}$ background conductivity matrix on a measurable set well within the domain, and we assume $\left(\gamma_{n}-\gamma_{0}\right)\gamma_{n}^{-1}\left(\gamma_{n}-\gamma_{0}\right)\to0$ in $L^{1}(\Omega)$. Adapting the limit measure, we show that the general representation formula introduced for bounded contrasts in this article can be extended to unbounded sequences of matrix valued conductivities.
Fichier principal
Vignette du fichier
2022-Capdeboscq-Ong.pdf (651.05 Ko) Télécharger le fichier
Origine Fichiers éditeurs autorisés sur une archive ouverte

Dates et versions

hal-03171353 , version 1 (16-03-2021)
hal-03171353 , version 2 (22-02-2022)

Licence

Identifiants

Citer

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, 2022, 360, pp.127--150. ⟨10.5802/crmath.273⟩. ⟨hal-03171353v2⟩
81 Consultations
71 Téléchargements

Altmetric

Partager

More