Homogenization of variational problems in manifold valued Sobolev spaces

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, Fonseca, Maly and Trivisa \cite{DFMT}. 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 \cite{BM}.

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