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Journal Articles ESAIM: Control, Optimisation and Calculus of Variations Year : 2010

Homogenization of variational problems in manifold valued Sobolev spaces

Vincent Millot

Abstract

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].

Dates and versions

hal-00265697 , version 1 (19-03-2008)

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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⟩
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