A Γ-CONVERGENCE APPROACH TO NON-PERIODIC HOMOGENIZATION OF STRONGLY ANISOTROPIC FUNCTIONALS
Annalisa Baldi, Maria Carla Tesi · Mathematical Models and Methods in Applied Sciences · 2004
In this work we present a homogenization result for a class of degenerate elliptic functionals mimicking strongly anisotropic media. We study the limit as ε→0 of the functionals [Formula: see text] where, for any ε>0, αε:ℝn×ℝn→ℝ, αε(x,ξ)≈ε(x)ξ,ξ>p/2-1, Aε∈Mn×n(ℝ) being measurable non-negative matrices such that [Formula: see text] almost everywhere, p>1. To take into account the anisotropy of the media we consider two families of weight functions reasonably different, λε and Λε, possibly degenerate or singular, such that: [Formula: see text] The convergence to the homogenized problem is obtained by a classical approach of Γ-convergence.