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Homogenization of variational problems in manifold valued Sobolev spaces

2009; EDP Sciences; Volume: 16; Issue: 4 Linguagem: Inglês

10.1051/cocv/2009025

1292-8119

Jean‐François Babadjian, Vincent Millot,

Composite Material Mechanics

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].