Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Gabriella Sebestyén

Dept. of Analysis, Faculty of Science, Eötvös Loránd University, 1117 Budapest, Hungary

Keywords

  • Gradients
  • quasiconvexity
  • rank-one convexity
  • laminates

Mathematics Subject Classification

49J10, 49K10

Suggested citation

G. Sebestyén, L. Székelyhidi Jr.. “Laminates Supported on Cubes.” Journal of Convex Analysis 24 (2017), No. 4, 1217–1237.

Copyright Heldermann Verlag 2017