Let be a compact set, let be its rank-one convex hull, and let be its lamination convex hull. It is shown that the mapping is not upper semicontinuous on the diagonal matrices in , which was a problem left by Kolář. This is followed by an example of a -point set of symmetric matrices with non-compact lamination hull. Finally, another -point set is constructed, which has connected, compact and strictly smaller than .
Keywords: Lamination convexity, rank-one convexity
@article{COCV_2018__24_4_1503_0, author = {Harris, Terence L.J.}, title = {Upper semicontinuity of the lamination hull}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {1503--1510}, publisher = {EDP-Sciences}, volume = {24}, number = {4}, year = {2018}, doi = {10.1051/cocv/2017033}, mrnumber = {3922434}, zbl = {1411.26015}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2017033/} }
TY - JOUR AU - Harris, Terence L.J. TI - Upper semicontinuity of the lamination hull JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2018 SP - 1503 EP - 1510 VL - 24 IS - 4 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2017033/ DO - 10.1051/cocv/2017033 LA - en ID - COCV_2018__24_4_1503_0 ER -
%0 Journal Article %A Harris, Terence L.J. %T Upper semicontinuity of the lamination hull %J ESAIM: Control, Optimisation and Calculus of Variations %D 2018 %P 1503-1510 %V 24 %N 4 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2017033/ %R 10.1051/cocv/2017033 %G en %F COCV_2018__24_4_1503_0
Harris, Terence L.J. Upper semicontinuity of the lamination hull. ESAIM: Control, Optimisation and Calculus of Variations, Volume 24 (2018) no. 4, pp. 1503-1510. doi : 10.1051/cocv/2017033. http://archive.numdam.org/articles/10.1051/cocv/2017033/
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