Abstract
We study the asymptotic behavior, as ε → 0 , of u ε solutions to a nonlinear elliptic equation with nonstandard growth condition in domains containing a grid-type microstructure F ε that is concentrated in an arbitrary small neighborhood of a given hypersurface Γ. We assume that u ε = A ε on ∂ F ε , where A ε is an unknown constant. The macroscopic equation and a nonlocal transmission condition on Γ are obtained by the variational homogenization technique in the framework of Sobolev spaces with variables exponents. This result is then illustrated by a periodic example. To cite this article: B. Amaziane et al., C. R. Mecanique 337 (2009).
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