|Publication ahead of print|
|Published online||11 July 2018|
Upper semicontinuity of the lamination hull★
School of Mathematics and Statistics, University of New South Wales,
NSW 2052, Australia
2 Department of Mathematics, University of Illinois, Urbana IL 61801, USA.
a Corresponding author: email@example.com
Revised: 18 March 2017
Accepted: 21 April 2017
Let K ⊆ ℝ2×2 be a compact set, let Krc 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 ℝ2×2, 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 Krc.
Mathematics Subject Classification: 49J45 / 52A30
Key words: Lamination convexity / rank-one convexity
© EDP Sciences, SMAI 2018
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.