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Homogenization of variational problems in manifold valued Sobolev spaces

Published online by Cambridge University Press:  31 July 2009

Jean-François Babadjian  and
Vincent Millot
Jean-François Babadjian
Affiliation:
CMAP, UMR 7641, École polytechnique, 91128 Palaiseau, France. babadjian@cmap.polytechnique.fr
Vincent Millot
Affiliation:
Université Paris Diderot – Paris 7, CNRS, UMR 7598, Laboratoire Jacques-Louis Lions, 75005 Paris, France. millot@math.jussieu.fr
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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].

Keywords

HomogenizationΓ-convergencemanifold valued maps
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 16 , Issue 4 , October 2010 , pp. 833 - 855
Copyright
© EDP Sciences, SMAI, 2009

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