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

被引：48

作者：

Ammari, Habib ^{[2
,3
]}

Kang, Hyeonbae ^{[1
]}

Lee, Hyundae ^{[1
]}

Lim, Mikyoung ^{[4
]}

Zribi, Habib ^{[5
]}

机构：

[1] Inha Univ, Dept Math, Inchon 402751, South Korea

[2] CNRS, UMR 7587, Lab Ondes & Acoust, F-75231 Paris 05, France

[3] ESPCI, F-75231 Paris 05, France

[4] Korea Adv Inst Sci & Technol, Dept Math Sci, Taejon 305701, South Korea

[5] Seoul Natl Univ, Dept Math Sci, Seoul 151747, South Korea

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2009年 / 247卷 / 11期

关键词：

Conductivity problem; Gradient estimates; Decomposition; Extreme conductivity; Blow-up; Permittivity; CONDUCTIVITY PROBLEM; FIBER COMPOSITES; STRESSES;

D O I：

10.1016/j.jde.2009.08.005

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：2897 / 2912

页数：16

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