We study the weak* lower semicontinuity of functionals of the form
where is a bounded open set, and �� is a constant-rank partial differential operator. The notion of ��-Young quasiconvexity, which is introduced here, provides a sufficient condition when is only lower semicontinuous. We also establish necessary conditions for weak* lower semicontinuity. Finally, we discuss the divergence and curl-free cases and, as an application, we characterise the strength set in the context of electrical resistivity.
DOI: 10.1051/cocv/2014058
Keywords: Supremal functionals, Γ-convergence, Lp-approximation, lower semicontinuity, 𝒜-quasiconvexity
@article{COCV_2015__21_4_1053_0, author = {Ansini, Nadia and Prinari, Francesca}, title = {On the lower semicontinuity of supremal functional under differential constraints}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {1053--1075}, publisher = {EDP-Sciences}, volume = {21}, number = {4}, year = {2015}, doi = {10.1051/cocv/2014058}, mrnumber = {3395755}, zbl = {1336.49015}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2014058/} }
TY - JOUR AU - Ansini, Nadia AU - Prinari, Francesca TI - On the lower semicontinuity of supremal functional under differential constraints JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2015 SP - 1053 EP - 1075 VL - 21 IS - 4 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2014058/ DO - 10.1051/cocv/2014058 LA - en ID - COCV_2015__21_4_1053_0 ER -
%0 Journal Article %A Ansini, Nadia %A Prinari, Francesca %T On the lower semicontinuity of supremal functional under differential constraints %J ESAIM: Control, Optimisation and Calculus of Variations %D 2015 %P 1053-1075 %V 21 %N 4 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2014058/ %R 10.1051/cocv/2014058 %G en %F COCV_2015__21_4_1053_0
Ansini, Nadia; Prinari, Francesca. On the lower semicontinuity of supremal functional under differential constraints. ESAIM: Control, Optimisation and Calculus of Variations, Volume 21 (2015) no. 4, pp. 1053-1075. doi : 10.1051/cocv/2014058. http://archive.numdam.org/articles/10.1051/cocv/2014058/
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