We characterize generalized Young measures, the so-called DiPerna-Majda measures which are generated by sequences of gradients. In particular, we precisely describe these measures at the boundary of the domain in the case of the compactification of ℝm × n by the sphere. We show that this characterization is closely related to the notion of quasiconvexity at the boundary introduced by Ball and Marsden [J.M. Ball and J. Marsden, Arch. Ration. Mech. Anal. 86 (1984) 251-277]. As a consequence we get new results on weak W1,2(Ω; ℝ3) sequential continuity of u → a· [Cof∇u] ϱ, where Ω ⊂ ℝ3 has a smooth boundary and a,ϱ are certain smooth mappings.
Mots-clés : bounded sequences of gradients, concentrations, oscillations, quasiconvexity at the boundary, weak lower semicontinuity
@article{COCV_2013__19_3_679_0,
author = {Kru\v{z}{\'\i}k, Martin},
title = {Quasiconvexity at the boundary and concentration effects generated by gradients},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {679--700},
publisher = {EDP-Sciences},
volume = {19},
number = {3},
year = {2013},
doi = {10.1051/cocv/2012028},
mrnumber = {3092357},
zbl = {1277.49014},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2012028/}
}
TY - JOUR AU - Kružík, Martin TI - Quasiconvexity at the boundary and concentration effects generated by gradients JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2013 SP - 679 EP - 700 VL - 19 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2012028/ DO - 10.1051/cocv/2012028 LA - en ID - COCV_2013__19_3_679_0 ER -
%0 Journal Article %A Kružík, Martin %T Quasiconvexity at the boundary and concentration effects generated by gradients %J ESAIM: Control, Optimisation and Calculus of Variations %D 2013 %P 679-700 %V 19 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2012028/ %R 10.1051/cocv/2012028 %G en %F COCV_2013__19_3_679_0
Kružík, Martin. Quasiconvexity at the boundary and concentration effects generated by gradients. ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 3, pp. 679-700. doi : 10.1051/cocv/2012028. http://www.numdam.org/articles/10.1051/cocv/2012028/
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