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manifold valued maps

ESAIM: Control, Optimisation and Calculus of Variations (1)

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Homogenization of variational problemsin manifold valued Sobolev spaces
Jean-François Babadjian, Vincent Millot
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 16 / Issue 4 / October 2010

Published online by Cambridge University Press:

31 July 2009, pp. 833-855

Print publication:

October 2010
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Homogenization of integral functionals is studiedunder the constraint that admissible maps have to take their valuesinto a given smooth manifold. The notion of tangentialhomogenization is defined by analogy with the tangentialquasiconvexity introduced by Dacorogna et al. [Calc. Var. Part. Diff. Eq. 9 (1999) 185–206]. For energies with superlinear or linear growth, aΓ-convergence result is established in Sobolev spaces, thehomogenization problem in the space of functions of boundedvariation being the object of [Babadjian and Millot, Calc. Var. Part. Diff. Eq.36 (2009) 7–47].