On Keller Theorem for Anisotropic Media

Abstract

The Keller theorem in the problem of effective conductivity in anisotropic two-dimensional (2D) many-component composites makes it possible to establish a simple inequality $σ_{\sf is}^e(σ^{-1}_i)\cdot σ_{\sf is}^e(σ_k)> 1$ for the isotropic part $σ_{\sf is}^e(σ_k)$ of the 2-nd rank symmetric tensor ${\widehat σ}_{i,j}^e$ of effective conductivity.