Decomposition theorems and fine estimates for electrical fields in the presence of closely located circular inclusions

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When two inclusions get closer and their conductivities degenerate to zero or infinity, the gradient of the solution to the conductivity equation blows up in general. In this paper, we show that the solution to the conductivity equation can be decomposed into two parts in an explicit form: one of them has a bounded gradient and the gradient of the other part blows Lip. Using the decomposition. we derive the best possible estimates for the blow-up of the gradient. We then consider the case when the inclusions have positive permittivities. We show quantitatively that in this case the size of the blow-up is reduced. (C) 2009 Elsevier Inc. All rights reserved.
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Issue Date
2009-12
Language
English
Article Type
Article
Keywords

CONDUCTIVITY PROBLEM; FIBER COMPOSITES; STRESSES

Citation

JOURNAL OF DIFFERENTIAL EQUATIONS, v.247, no.11, pp.2897 - 2912

ISSN
0022-0396
DOI
10.1016/j.jde.2009.08.005
URI
http://hdl.handle.net/10203/97674
Appears in Collection
MA-Journal Papers(저널논문)
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