Displaying similar documents to “A variational approach to the local character of G -closure : the convex case”

Homogenization of periodic nonconvex integral functionals in terms of Young measures

Omar Anza Hafsa, Jean-Philippe Mandallena, Gérard Michaille (2006)

ESAIM: Control, Optimisation and Calculus of Variations

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Homogenization of periodic functionals, whose integrands possess possibly multi-well structure, is treated in terms of Young measures. More precisely, we characterize the Γ -limit of sequences of such functionals in the set of Young measures, extending the relaxation theorem of Kinderlherer and Pedregal. We also make precise the relationship between our homogenized density and the classical one.

Homogenization of micromagnetics large bodies

Giovanni Pisante (2004)

ESAIM: Control, Optimisation and Calculus of Variations

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A homogenization problem related to the micromagnetic energy functional is studied. In particular, the existence of the integral representation for the homogenized limit of a family of energies ℰ ε ( m ) = ∫ Ω φ x , x ε , m ( x ) d x - ∫ Ω h e ( x ) · m ( x ) d x + 1 2 ∫ ℝ 3 | ∇ u ( x ) | 2 d x of a large ferromagnetic body is obtained.

Homogenization of variational problems in manifold valued Sobolev spaces

Jean-François Babadjian, Vincent Millot (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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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 [  (1999) 185–206]. For energies with superlinear or linear growth, a -convergence result is established in Sobolev spaces, the homogenization problem in the space of functions of bounded variation being the object of...

A characterization of gradient Young-concentration measures generated by solutions of Dirichlet-type problems with large sources

Gisella Croce, Catherine Lacour, Gérard Michaille (2009)

ESAIM: Control, Optimisation and Calculus of Variations

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We show how to capture the gradient concentration of the solutions of Dirichlet-type problems subjected to large sources of order 1 ε concentrated on an ε -neighborhood of a hypersurface of the domain. To this end we define the gradient Young-concentration measures generated by sequences of finite energy and establish a very simple characterization of these measures.