Affiliations: Universite Montpellier II, UMR-CNRS 5508, LMGC, Place Eugène Bataillon, 34095 Montpellier, France E-mail: [email protected] | Laboratoire de Mécanique, Physique et Modélisation Mathématique, Universite de Médéa, LMP2M, Quartier Ain-D'Heb, Médéa 26000, Algerie. E-mail: [email protected] | Laboratoire MIPA, Universite de Nîmes, Site des Carmes, Place Gabriel Péri, 30021 Nîmes, France. E-mail: [email protected]
Abstract: We study homogenization by Γ-convergence of functionals of type ∫ΩW(x/ε,∇ϕ(x)) dx, where Omega⊂RN is a bounded open set, ϕ∈W1,p(Omega;Rm) and p>1, when the 1-periodic integrand W :RN×Mm×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.
