Journal of Convex Analysis 24 (2017), No. 4, 1217--1237
Copyright Heldermann Verlag 2017
Laminates Supported on Cubes
Dept. of Analysis, Faculty of Science, Eötvös Loránd University, 1117 Budapest, Hungary
László Székelyhidi Jr.
Mathematisches Institut, Universität Leipzig, Augustusplatz 10, 04109 Leipzig, Germany
We study the relationship between rank-one convexity and quasiconvexity in the space of 2×2 matrices. We show that a certain procedure for constructing homogeneous gradient Young measures from periodic deformations, that arises from V. Sverák's celebrated counterexample in higher dimensions, always yields laminates in the 2×2 case.
Keywords: Gradients, quasiconvexity, rank-one convexity, laminates.
MSC: 49J10, 49K10
[ Fulltext-pdf (156 KB)] for subscribers only.