In this paper we study the lower semicontinuity problem for a supremal functional of the form with respect to the strong convergence in , furnishing a comparison with the analogous theory developed by Serrin for integrals. A sort of Mazur’s lemma for gradients of uniformly converging sequences is proved.
Keywords: supremal functionals, lower semicontinuity, level convexity, calculus of variations, Mazur's lemma
@article{COCV_2003__9__135_0, author = {Gori, Michele and Maggi, Francesco}, title = {On the lower semicontinuity of supremal functionals}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {135--143}, publisher = {EDP-Sciences}, volume = {9}, year = {2003}, doi = {10.1051/cocv:2003005}, mrnumber = {1957094}, zbl = {1066.49010}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv:2003005/} }
TY - JOUR AU - Gori, Michele AU - Maggi, Francesco TI - On the lower semicontinuity of supremal functionals JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2003 SP - 135 EP - 143 VL - 9 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv:2003005/ DO - 10.1051/cocv:2003005 LA - en ID - COCV_2003__9__135_0 ER -
%0 Journal Article %A Gori, Michele %A Maggi, Francesco %T On the lower semicontinuity of supremal functionals %J ESAIM: Control, Optimisation and Calculus of Variations %D 2003 %P 135-143 %V 9 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv:2003005/ %R 10.1051/cocv:2003005 %G en %F COCV_2003__9__135_0
Gori, Michele; Maggi, Francesco. On the lower semicontinuity of supremal functionals. ESAIM: Control, Optimisation and Calculus of Variations, Volume 9 (2003), pp. 135-143. doi : 10.1051/cocv:2003005. http://archive.numdam.org/articles/10.1051/cocv:2003005/
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