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Optimal Estimates for the Electric Field in Two-Dimensions
 

Summary: Optimal Estimates for the Electric Field in
Two-Dimensions
Habib Ammari (ammari@cmapx.polytechnique.fr)
Hyeonbae Kang (hkang@math.snu.ac.kr)
Hyundae Lee (hdlee@math.snu.ac.kr)
Jungwook Lee (wook9@snu.ac.kr)
Mikyoung Lim (mklim@cmapx.polytechnique.fr)
R´esum´e
L'objet de cet article est d'´etablir des estimations pr´ecises sur le champ ´electrique
dans des cas o`u deux objets conducteurs sont proches l'un de l'autre. La nouveaut´e
de nos estimations est qu'elles donnent des bornes optimales non seulement en fonc-
tion de la distance qui s´epare les objets conducteurs mais ´egalement en fonction de
leurs conductivit´es dans les cas o`u elles d´eg´en`erent.
Abstract
We establish both upper and lower bounds on the electric field in the case
where two circular conductivity inclusions are very close but not touching. We
also obtain such bounds when a circular inclusion is very close to the bound-
ary of a circular domain which contains the inclusion. The novelty of these
estimates, which improve and make complete our earlier results in [6], is that
they give an optimal information about the blow-up of the electric field as the

  

Source: Ammari, Habib - Centre de Mathématique Appliquées, École Polytechnique

 

Collections: Mathematics