Geodesic
Homogenization of variational problems in manifold valued Sobolev spaces
ESAIM: Control, Optimisation and Calculus of Variations, Tome 16 (2010) no. 4, pp. 833-855

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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].

DOI : 10.1051/cocv/2009025
Classification : 74Q05, 49J45, 49Q20
Keywords: homogenization, Γ-convergence, manifold valued maps 
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     author = {Babadjian, Jean-Fran\c{c}ois and Millot, Vincent},
     title = {Homogenization of variational problems in manifold valued {Sobolev} spaces},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {833--855},
     publisher = {EDP-Sciences},
     volume = {16},
     number = {4},
     year = {2010},
     doi = {10.1051/cocv/2009025},
     mrnumber = {2744153},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2009025/}
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Babadjian, Jean-François; Millot, Vincent. Homogenization of variational problems in manifold valued Sobolev spaces. ESAIM: Control, Optimisation and Calculus of Variations, Tome 16 (2010) no. 4, pp. 833-855. doi: 10.1051/cocv/2009025

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