Displaying similar documents to “A-quasiconvexity : weak-star convergence and the gap”

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...

Equi-integrability results for 3D-2D dimension reduction problems

Marian Bocea, Irene Fonseca (2002)

ESAIM: Control, Optimisation and Calculus of Variations

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3D-2D asymptotic analysis for thin structures rests on the mastery of scaled gradients ∇ α u ε | 1 ε ∇ 3 u ε bounded in L p ( Ω ; ℝ 9 ) , 1 < p < + ∞ . Here it is shown that, up to a subsequence, u ε may be decomposed as w ε + z ε , where z ε carries all the concentration effects, i.e. ∇ α w ε | 1 ε ∇ 3 w ε p is equi-integrable, and w ε captures the oscillatory behavior, i.e. z ε → 0 in measure. In addition, if { u ε } is a recovering sequence then z ε = z ε ( x α ) nearby ∂ Ω .