Equi-integrability results for 3D-2D dimension reduction problems
ESAIM: Control, Optimisation and Calculus of Variations, Tome 7 (2002), pp. 443-470.

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.

DOI : 10.1051/cocv:2002063
Classification : 49J45, 74B20, 74G10, 74K15, 74K35
Mots clés : equi-integrability, dimension reduction, lower semicontinuity, maximal function, oscillations, concentrations, quasiconvexity 
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     title = {Equi-integrability results for {3D-2D} dimension reduction problems},
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     pages = {443--470},
     publisher = {EDP-Sciences},
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     mrnumber = {1925037},
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Bocea, Marian; Fonseca, Irene. Equi-integrability results for 3D-2D dimension reduction problems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 7 (2002), pp. 443-470. doi : 10.1051/cocv:2002063. http://www.numdam.org/articles/10.1051/cocv:2002063/

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