Nonlinear double porosity models with non-standard growth

Abstract

We study the solutions to quasilinear elliptic equations with high contrast coefficients. The energy formulation leads to work with variable exponent Lebesgue spaces L p ε ( ⋅ ) in domains with a complex microstructure scaled by a small parameter ε. We derive rigorously the corresponding homogenized problem. It is completely described in terms of local energy characteristics of the original domain. To cite this article: C. Choquet, L. Pankratov, C. R. Mecanique 337 (2009).