Stochastic homogenization for an integral functional of a quasiconvex function with linear growth

Article type: Research Article

Authors: Abddaimi, Y. | Michaille, G.^; | Licht, C.

Affiliations: Laboratoire d'Analyse Convexe, Université Montpellier II, C.C.051 Place Eugène Bataillon, 34095 Montpellier Cedex 05, France | Laboratoire de Mécanique et Génie Civil, Université Montpellier II, C.C.048 Place Eugène Bataillon, 34095 Montpellier Cedex 05, France

Note: [] Corresponding author. Fax: +33 67 14 35 58; E-mail: micha@math.univ-montpz.fr.

Abstract: We establish the epiconvergence (or Γ-convergence) for the strong topology of L1(O,RN) of a sequence of random integral functionals ∫Of(ω)(x/ε,∇u(x)) dx defined in the space W1,1(O,RN). Our method uses an improvement of a convergence result concerning subadditive processes and a recent technique of blow-up combined with the rank one property of the singular measure Dsu.

Keywords: Homogenization, epiconvergence, stochastic processes, ergodic theory

DOI: 10.3233/ASY-1997-15203

Journal: Asymptotic Analysis, vol. 15, no. 2, pp. 183-202, 1997