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

Abstract

3D-2D asymptotic analysis for thin structures rests on the mastery of scaled gradients bounded in Lp(Ω;ℝ9), 1 < p < +∞. Here it is shown that, up to a subsequence, uε may be decomposed as wε+zε, where zε carries all the concentration effects, i.e. (Formula Presented) is equi-integrable, and wε captures the oscillatory behavior, i.e. zε → 0 in measure. In addition, if {uε} is a recovering sequence then zε = zε(xα) nearby ∂Ω. © 2002 EDP Sciences, SMAI.