Change of Sign of the Corrector’s Determinant for Homogenization in Three-Dimensional Conductivity
Change of Sign of the Corrector’s Determinant for Homogenization in Three-Dimensional Conductivity
复制标题
三维电导率均匀化校正器行列式的符号变化
DOI：
10.1007/s00205-004-0315-8
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发表时间：
2004
影响因子：
2.5
通讯作者：
V. Nesi
中科院分区：
文献类型：
--
作者：
M. Briane;G. Milton;V. Nesi
摘要：本文研究导电复合材料中局部电场行列式的正性。我们通过文献[1]知道，对于任何周期结构，正性在两个维度上都成立。使用与[11]不同的方法，我们证明了对于任何维度的层状微结构也是如此。然而，这是本文的主要结果，我们提供了一个行列式变号的两相三维周期复合材料的例子。
Abstract.In this paper we study the positivity of the determinant of the local electric field in a conducting composite. We know by [1] that the positivity holds true in two dimensions for any periodic structure. Using a different approach from [11] we prove that is also the case for a laminate microstructure in any dimension. However, and this is the main result of the paper, we provide an example of a two-phase three-dimensional periodic composite for which the determinant changes sign.