Hostname: page-component-76fb5796d-dfsvx Total loading time: 0 Render date: 2024-04-29T06:02:56.727Z Has data issue: false hasContentIssue false
  • English
  • Français

Examples of rank-one convex functions

Published online by Cambridge University Press:  14 November 2011

Vladimír Šverák
Vladimír Šverák
Affiliation:
Katedra Matematické Analýzy, MFF-UK, Sokolovska 83, 18600 Prague 8, Czechoslovakia
Get access Rights & Permissions [Opens in a new window]

Synopsis

We construct rank-one convex functions which are not convex and have linear growth at infinity. We show that these functions could be useful in some problems concerning weak convergence of gradients if we were able to prove that they are quasiconvex. This question, however, seems to be open.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 114 , Issue 3-4 , 1990 , pp. 237 - 242
Copyright
Copyright © Royal Society of Edinburgh 1990

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Acerbi, E. and Fusco, N.. Semicontinuity problems in the calculus of variations. Arch. Rational Mech. Anal. 86 (1984), 125–145.CrossRefGoogle Scholar
2Ball, J. M. and Murat, F. (in preparation).Google Scholar
3Ball, J. M. and James, R. D.. Fine phase mixtures as minimizers of energy. Arch Rational Mech. Anal. 100 (1987) 13–52.CrossRefGoogle Scholar
4Morrey, C. B.. Multiple Integrals in the Calculus of Variations (Berlin's Springer, 1966).CrossRefGoogle Scholar
5Morrey, C. B.. Quasi-convexity and lower semicontinuity of multiple integrals. Pacific J. Math. 2 (1952) 25–53.CrossRefGoogle Scholar
6Kewei, Zhang. Biting theorems for Jacobians and their applications. Ann. Inst. H. Poincaré Anal. Non Linéaire (to appear).Google Scholar