An asymptotic formula for the voltage potential in a perturbed ε-periodic composite medium containing misplaced inclusions of size ε

Abstract

We consider composite media made of homogeneous inclusions with C 1,α ,boundaries. Our goal is to compare the potential u ε in a perfectly periodic composite with the potential u ε, d , of a perturbed periodic medium, where the periodicity defects consist of misplaced inclusions. We give an asymptotic expansion of the difference u ε, d − u ε away from the defects and show that, to first order, a misplaced inclusion manifests itself via a polarization tensor, which is characterized.