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; 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 : https://doi.org/10.1051/cocv:2002063
Classification : 49J45,  74B20,  74G10,  74K15,  74K35
Mots clés : equi-integrability, dimension reduction, lower semicontinuity, maximal function, oscillations, concentrations, quasiconvexity
@article{COCV_2002__7__443_0,
     author = {Bocea, Marian and Fonseca, Irene},
     title = {Equi-integrability results for 3D-2D dimension reduction problems},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {443--470},
     publisher = {EDP-Sciences},
     volume = {7},
     year = {2002},
     doi = {10.1051/cocv:2002063},
     zbl = {1044.49010},
     mrnumber = {1925037},
     language = {en},
     url = {http://www.numdam.org/item/COCV_2002__7__443_0/}
}
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/item/COCV_2002__7__443_0/

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