Free access
Volume 12, Number 2, April 2006
Page(s) 253 - 270
Published online 22 March 2006
  1. E. Aranda and P. Pedregal, On the computation of the rank-one convex hull of a function. SIAM J. Sci. Comput. 22 (2000) 1772–1790 (electronic). [CrossRef] [MathSciNet]
  2. S. Aubry, M. Fago and M. Ortiz, A constrained sequential-lamination algorithm for the simulation of sub-grid microstructure in martensitic materials. Comput. Methods Appl. Mech. Engrg. 192 (2003) 2823–2843. [CrossRef] [MathSciNet]
  3. M. Chlebík and B. Kirchheim, Rigidity for the four gradient problem. J. Reine Angew. Math. 551 (2002) 1–9. [MathSciNet]
  4. B. Dacorogna, Direct methods in the calculus of variations. Applied Mathematical Sciences, Springer-Verlag, Berlin 78 (1989).
  5. G. Dolzmann, Numerical computation of rank-one convex envelopes. SIAM J. Numer. Anal. 36 (1999) 1621–1635 (electronic). [CrossRef] [MathSciNet]
  6. Da.R. Grayson and M.E. Stillman, Macaulay 2, a software system for research in algebraic geometry. Available at
  7. J. Harris, Algebraic geometry. Springer-Verlag, New York (1995). A first course, Corrected reprint of the 1992 original.
  8. B. Kirchheim, Rigidity and geometry of microstructures. Lecture notes 16/2003, Max Planck Institute for Mathematics in the Sciences, Leipzig (2003).
  9. B. Kirchheim, S. Müller and V. Šverák, Studying nonlinear pde by geometry in matrix space, in Geometric analysis and nonlinear partial differential equations. Springer, Berlin (2003) 347–395.
  10. C.-F. Kreiner, Algebraic methods for convexity notions in the calculus of variations. Master's thesis, Technische Universität München, Zentrum Mathematik (2003).
  11. C.-F. Kreiner, J. Zimmer and I. Chenchiah, Towards the efficient computation of effective properties of microstructured materials. Comptes Rendus Mecanique 332 (2004) 169–174. [CrossRef]
  12. J. Matoušek and P. Plecháč, On functional separately convex hulls. Discrete Comput. Geom. 19 (1998) 105–130. [NASA ADS] [CrossRef] [EDP Sciences] [MathSciNet] [PubMed]
  13. S. Müller, Variational models for microstructure and phase transitions, in Calculus of variations and geometric evolution problems (Cetraro, 1996). Springer, Berlin, Lect. Notes Math. 1713 (1999) 85–210.
  14. S. Müller and V. Šverák, Unexpected solutions of first and second order partial differential equations, in Proceedings of the International Congress of Mathematicians, Vol. II (Berlin, 1998), Extra Vol. II (1998) 691–702.
  15. L. Råde and B. Westergren, Mathematics handbook for science and engineering. Springer-Verlag, Berlin, fourth edition (1999).
  16. V. Scheffer, Regularity and irregularity of solutions to nonlinear second order elliptic systems of partial differential equations and inequalities. Ph.D. thesis, Princeton University (1974).
  17. V. Šverák, Rank-one convexity does not imply quasiconvexity. Proc. Roy. Soc. Edinburgh Sect. A 120 (1992) 185–189. [MathSciNet]
  18. L. Székelyhidi Jr, Rank-one convex hulls in Formula . Calc. Var. Partial Differ. Equ. 22 (2005) 253–281.
  19. L. Tartar, Some remarks on separately convex functions, in Microstructure and phase transition. Springer, New York, IMA Vol. Math. Appl. 54 (1993) 191–204.