Homogenization of variational problems in manifold valued Sobolev spaces

Jean-François Babadjian; Vincent Millot

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 16, Issue: 4, page 833-855
  • ISSN: 1292-8119

Abstract

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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].

How to cite

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Babadjian, Jean-François, and Millot, Vincent. "Homogenization of variational problems in manifold valued Sobolev spaces." ESAIM: Control, Optimisation and Calculus of Variations 16.4 (2010): 833-855. <http://eudml.org/doc/250739>.

@article{Babadjian2010,
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]. },
author = {Babadjian, Jean-François, Millot, Vincent},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Homogenization; Γ-convergence; manifold valued maps; -convergence},
language = {eng},
month = {10},
number = {4},
pages = {833-855},
publisher = {EDP Sciences},
title = {Homogenization of variational problems in manifold valued Sobolev spaces},
url = {http://eudml.org/doc/250739},
volume = {16},
year = {2010},
}

TY - JOUR
AU - Babadjian, Jean-François
AU - Millot, Vincent
TI - Homogenization of variational problems in manifold valued Sobolev spaces
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/10//
PB - EDP Sciences
VL - 16
IS - 4
SP - 833
EP - 855
AB - 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].
LA - eng
KW - Homogenization; Γ-convergence; manifold valued maps; -convergence
UR - http://eudml.org/doc/250739
ER -

References

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