# American Institute of Mathematical Sciences

December  2020, 15(4): 581-603. doi: 10.3934/nhm.2020015

## Perturbation analysis of the effective conductivity of a periodic composite

 1 Dipartimento di Matematica 'Tullio Levi-Civita', Università degli Studi di Padova, Via Trieste 63, 35121 Padova, Italy 2 Dipartimento di Scienze Molecolari e Nanosistemi, Università Ca' Foscari Venezia, via Torino 155, 30172 Venezia Mestre, Italy

* Corresponding author: Paolo Musolino

Received  March 2020 Revised  June 2020 Published  July 2020

We consider the effective conductivity $\lambda^{\mathrm{eff}}$ of a periodic two-phase composite obtained by introducing into an infinite homogeneous matrix a periodic set of inclusions of a different material. Then we study the behavior of $\lambda^{\mathrm{eff}}$ upon perturbation of the shape of the inclusions, of the periodicity structure, and of the conductivity of each material.

Citation: Paolo Luzzini, Paolo Musolino. Perturbation analysis of the effective conductivity of a periodic composite. Networks & Heterogeneous Media, 2020, 15 (4) : 581-603. doi: 10.3934/nhm.2020015
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##### References:
The sets $\mathbb{S}_{q}[q\mathbb{I}[\phi]]^-$, $\mathbb{S}_{q}[q\mathbb{I}[\phi]]$, and $q\phi(\partial\Omega)$ in case $n = 2$