## Homogenization of a non-periodic material.(English)Zbl 0835.35016

Summary: We study the homogenization of a non-periodic material of $$\mathbb{R}^N$$ in the conductivity case. This material consists of spherical balls of radius $$\varepsilon$$ ($$\varepsilon$$ is a parameter which will converge to $$0$$) and centered at the points $$\theta(k\varepsilon),k\in \mathbb{Z}^N$$, where $$\theta$$ is a diffeomorphism of $$\mathbb{R}^N$$.
We obtain homogenized material whose coefficients depend on $$\nabla \theta\circ \theta^{- 1}$$. We prove the result by comparing this material to a material which is periodic in domains of size $$\varepsilon^\gamma$$, $$1/2< \gamma< 1$$.

### MSC:

 35B27 Homogenization in context of PDEs; PDEs in media with periodic structure 35J20 Variational methods for second-order elliptic equations

### Keywords:

non-periodic material