On a homogenization technique for singular integrals
Omar Anza Hafsa, Mohamed Lamine Leghmizi, Jean-Philippe Mandallena · Asymptotic Analysis · 2011
We study homogenization by Γ-convergence of functionals of type ∫ Ω W(x/ε,∇ϕ(x)) dx, where Omega⊂R N is a bounded open set, ϕ∈W 1,p (Omega;R m ) and p>1, when the 1-periodic integrand W :R N ×M m×N →[0,+∞] is not of p-polynomial growth. Our homogenization technique can be applied when m=N and W has a singular behavior of type W(x,ξ)→+∞ as det ξ→0. However, our technique is not consistent with the constraint W(x,ξ)=+∞ if and only if det ξ≤0.