Upper semicontinuity of the lamination hull
ESAIM: Control, Optimisation and Calculus of Variations, Volume 24 (2018) no. 4, pp. 1503-1510.

Let  K 2 × 2 be a compact set, let K r c be its rank-one convex hull, and let L ( K ) be its lamination convex hull. It is shown that the mapping  K L ( K ) ¯ is not upper semicontinuous on the diagonal matrices in 2 × 2 , which was a problem left by Kolář. This is followed by an example of a 5 -point set of  2 × 2 symmetric matrices with non-compact lamination hull. Finally, another 5 -point set  K is constructed, which has L ( K ) connected, compact and strictly smaller than K r c .

DOI: 10.1051/cocv/2017033
Classification: 49J45, 52A30
Keywords: Lamination convexity, rank-one convexity
Harris, Terence L.J. 1

1
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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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