Homogenization of variational problems in manifold valued Sobolev spaces

Babadjian, Jean-François; Millot, Vincent

ESAIM: Control, Optimisation and Calculus of Variations, Tome 16 (2010) no. 4, pp. 833-855.

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].

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