Homogenization of variational problems in manifold valued Sobolev spaces
CMAP, UMR 7641, École polytechnique, 91128 Palaiseau, France. email@example.com
2 Université Paris Diderot – Paris 7, CNRS, UMR 7598, Laboratoire Jacques-Louis Lions, 75005 Paris, France. firstname.lastname@example.org
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].
Mathematics Subject Classification: 74Q05 / 49J45 / 49Q20
Key words: Homogenization / Γ-convergence / manifold valued maps
© EDP Sciences, SMAI, 2009