We use DiPerna’s and Majda’s generalization of Young measures to describe oscillations and concentrations in sequences of gradients, , bounded in if and is a bounded domain with the extension property in . Our main result is a characterization of those DiPerna-Majda measures which are generated by gradients of Sobolev maps satisfying the same fixed Dirichlet boundary condition. Cases where no boundary conditions nor regularity of are required and links with lower semicontinuity results by Meyers and by Acerbi and Fusco are also discussed.
Mots clés : sequences of gradients, concentrations, oscillations, quasiconvexity
@article{COCV_2008__14_1_71_0, author = {Ka{\l}amajska, Agnieszka and Kru\v{z}{\'\i}k, Martin}, title = {Oscillations and concentrations in sequences of gradients}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {71--104}, publisher = {EDP-Sciences}, volume = {14}, number = {1}, year = {2008}, doi = {10.1051/cocv:2007051}, mrnumber = {2375752}, zbl = {1140.49009}, language = {en}, url = {http://www.numdam.org/articles/10.1051/cocv:2007051/} }
TY - JOUR AU - Kałamajska, Agnieszka AU - Kružík, Martin TI - Oscillations and concentrations in sequences of gradients JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2008 SP - 71 EP - 104 VL - 14 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv:2007051/ DO - 10.1051/cocv:2007051 LA - en ID - COCV_2008__14_1_71_0 ER -
%0 Journal Article %A Kałamajska, Agnieszka %A Kružík, Martin %T Oscillations and concentrations in sequences of gradients %J ESAIM: Control, Optimisation and Calculus of Variations %D 2008 %P 71-104 %V 14 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv:2007051/ %R 10.1051/cocv:2007051 %G en %F COCV_2008__14_1_71_0
Kałamajska, Agnieszka; Kružík, Martin. Oscillations and concentrations in sequences of gradients. ESAIM: Control, Optimisation and Calculus of Variations, Tome 14 (2008) no. 1, pp. 71-104. doi : 10.1051/cocv:2007051. http://www.numdam.org/articles/10.1051/cocv:2007051/
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