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MiS Preprint

Rank-One Convex Hulls in $\Bbb R^{2\times 2}$

László Székelyhidi


We study the rank-one convex hull of compact sets $K\subset\R^{2\times 2}$. We show that if $K$ contains no two matrices whose difference has rank one, and if $K$ contains no four matrices forming a $T_4$ configuration, then the rank-one convex hull $K^{rc}$ is equal to $K$. Furthermore, we give a simple numerical criterion for testing for $T_4$ configurations.

MSC Codes:
49J45, 52A30
rank-one convexity

Related publications

2005 Repository Open Access
László Székelyhidi

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

In: Calculus of variations and partial differential equations, 22 (2005) 3, pp. 253-281