Preprint 69/2003

Rank-One Convex Hulls in 2×2

László Székelyhidi

Contact the author: Please use for correspondence this email.
Submission date: 27. Jul. 2003
Pages: 30
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
Bibtex
MSC-Numbers: 49J45, 52A30
Keywords and phrases: rank-one convexity
Download full preprint: PDF (958 kB), PS ziped (459 kB)

Abstract:
We study the rank-one convex hull of compact sets formula9. We show that if K contains no two matrices whose difference has rank one, and if K contains no four matrices forming a formula15 configuration, then the rank-one convex hull formula17 is equal to K. Furthermore, we give a simple numerical criterion for testing for formula15 configurations.

23.06.2018, 02:11