Calculus of Variations and Partial Differential Equations

, Volume 22, Issue 3, pp 253–281

Rank-one convex hulls in \(\mathbb{R}^{2\times2}\)


DOI: 10.1007/s00526-004-0272-y

Cite this article as:
Székelyhidi, L. Calc. Var. (2005) 22: 253. doi:10.1007/s00526-004-0272-y


We study the rank-one convex hull of compact sets \(K\subset\mathbb{R}^{2\times2}\). We show that if K contains no two matrices whose difference has rank one, and if K contains no four matrices forming a T4 configuration, then the rank-one convex hull Krc is equal to K. Furthermore, we give a simple numerical criterion for testing for T4 configurations.

Copyright information

© Springer-Verlag Berlin/Heidelberg 2004

Authors and Affiliations

  1. 1.Institute for Advanced Study,PrincetonUSA