Optimal estimates for the electric field in two dimensions

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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 boundary of a circular domain which contains the inclusion. The novelty of these estimates, which improve and make complete our earlier results in [H. Ammari, H. Kang, M. Lim, Gradient estimates for solutions to the conductivity problem, Math. Ann. 332 (2005) 277-286], is that they give an optimal information about the blow-up of the electric field as the conductivities of the inclusions degenerate. (C) 2007 Elsevier Masson SAS. All rights reserved.
Publisher
GAUTHIER-VILLARS/EDITIONS ELSEVIER
Issue Date
2007-10
Language
English
Article Type
Article
Keywords

CONDUCTIVITY PROBLEM; FIBER COMPOSITES; REGULARITY; STRESSES

Citation

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, v.88, no.4, pp.307 - 324

ISSN
0021-7824
DOI
10.1016/j.matpur.2007.07.005
URI
http://hdl.handle.net/10203/90692
Appears in Collection
MA-Journal Papers(저널논문)
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