DiPerna’s and Majda’s generalization of Young measures is used to describe oscillations and concentrations in sequences of maps satisfying a linear differential constraint . Applications to sequential weak lower semicontinuity of integral functionals on -free sequences and to weak continuity of determinants are given. In particular, we state necessary and sufficient conditions for weak* convergence of det in measures on the closure of if in . This convergence holds, for example, under Dirichlet boundary conditions. Further, we formulate a Biting-like lemma precisely stating which subsets must be removed to obtain weak lower semicontinuity of along . Specifically, are arbitrarily thin “boundary layers”.
Keywords: concentrations, oscillations, Young measures
@article{COCV_2010__16_2_472_0, author = {Fonseca, Irene and Kru\v{z}{\'\i}k, Martin}, title = {Oscillations and concentrations generated by ${\mathcal {A}}$-free mappings and weak lower semicontinuity of integral functionals}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {472--502}, publisher = {EDP-Sciences}, volume = {16}, number = {2}, year = {2010}, doi = {10.1051/cocv/2009006}, mrnumber = {2654203}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2009006/} }
TY - JOUR AU - Fonseca, Irene AU - Kružík, Martin TI - Oscillations and concentrations generated by ${\mathcal {A}}$-free mappings and weak lower semicontinuity of integral functionals JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2010 SP - 472 EP - 502 VL - 16 IS - 2 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2009006/ DO - 10.1051/cocv/2009006 LA - en ID - COCV_2010__16_2_472_0 ER -
%0 Journal Article %A Fonseca, Irene %A Kružík, Martin %T Oscillations and concentrations generated by ${\mathcal {A}}$-free mappings and weak lower semicontinuity of integral functionals %J ESAIM: Control, Optimisation and Calculus of Variations %D 2010 %P 472-502 %V 16 %N 2 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2009006/ %R 10.1051/cocv/2009006 %G en %F COCV_2010__16_2_472_0
Fonseca, Irene; Kružík, Martin. Oscillations and concentrations generated by ${\mathcal {A}}$-free mappings and weak lower semicontinuity of integral functionals. ESAIM: Control, Optimisation and Calculus of Variations, Volume 16 (2010) no. 2, pp. 472-502. doi : 10.1051/cocv/2009006. http://archive.numdam.org/articles/10.1051/cocv/2009006/
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