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Journal of Convex Analysis 24 (2017), No. 4, 1217--1237
Copyright Heldermann Verlag 2017

Laminates Supported on Cubes

Gabriella Sebestyén
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

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