Homogenization of variational problems in manifold valued Sobolev spaces

Jean-François Babadjian (1) , Vincent Millot (2)

1 EDP - Equations aux Dérivées Partielles
2 LJLL - Laboratoire Jacques-Louis Lions

Homogenization of integral functionals is studied under the constraint that admissible maps have to take their values into a given smooth manifold. The notion of tangential homogenization is defined by analogy with the tangential quasiconvexity introduced by Dacorogna et al. [Calc. Var. Part. Diff. Eq. 9 (1999) 185-206]. For energies with superlinear or linear growth, a Γ-convergence result is established in Sobolev spaces, the homogenization problem in the space of functions of bounded variation being the object of [Babadjian and Millot, Calc. Var. Part. Diff. Eq. 36 (2009) 7-47].

Mots clés: Homogenization; Γ-convergence; manifold valued maps

Domaines: Equations aux dérivées partielles [math.AP]

Jean-François Babadjian, Vincent Millot. Homogenization of variational problems in manifold valued Sobolev spaces. ESAIM: Control, Optimisation and Calculus of Variations, 2010, 16 (4), pp.833-855. ⟨10.1051/cocv/2009025⟩. ⟨hal-00265697⟩