Rank-One Convex Hulls in ℝ2×2
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Submission date: 27. Jul. 2003
published in: Calculus of variations and partial differential equations, 22 (2005) 3, p. 253-281
DOI number (of the published article): 10.1007/s00526-004-0272-y
MSC-Numbers: 49J45, 52A30
Keywords and phrases: rank-one convexity
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We study the rank-one convex hull of compact sets . We show that if K contains no two matrices whose difference has rank one, and if K contains no four matrices forming a configuration, then the rank-one convex hull is equal to K. Furthermore, we give a simple numerical criterion for testing for configurations.