On the non-locality of quasiconvexity

Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

Volumn 16, Issue 1, 1999, Pages 1-13

  Kristensen, Jan ^a  

^a HERIOT WATT UNIVERSITY   (United Kingdom)

Author keywords

Quasiconvexity; Rank one convexity

Indexed keywords

EID: 0001921052     PISSN: 02941449     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0294-1449(99)80006-7     Document Type: Article

References (27)

1. J. J. ALIBERT and B. DACOROGNA, An example of a quasiconvex function not polyconvex in dimension two. Arch. Rat. Mech. Anal., Vol. 117, 1992, pp. 155-166.
2. J. M. BALL, Convexity conditions and existence theorems in nonlinear elasticity. Arch. Rat. Mech. Anal., Vol. 63, 1978, pp. 337-403.
3. J. M. BALL, Sets of gradients with no rank-one connections. J. Math. pures et appl., Vol. 69, 1990, pp. 241-259.
4. J. M. BALL and F. MURAT, Remarks on rank-one convexity and quasiconvexity. In Proceedings of the 1990 Dundee Conference on Differential Equations.
5. J. M. BALL, J. C. CURRIE and P. J. OLVER, Null Lagrangians, weak continuity, and variational problems of any order. J. Funct. Anal., Vol. 41, 1981, pp. 135-174.
6. B. DACOROGNA, "Direct Methods in the Calculus of Variations". 1989 (Berlin: Springer).
7. D. KINDERLEHRER and P. PEDREGAL, Characterizations of Young measures generated by gradients. Arch. Rat. Mech. Anal., Vol. 115, 1991, pp. 329-365.
8. J. KRISTENSEN. On quasiconvexification of locally bounded functions. Preprint, 1996.
9. J. KRISTENSEN. (In preparation).
10. J. MATOUSEK and P. PLECHAC, On functional separately convex hulls. Discrete and Computational Geometry (to appear).
11. N. G. MEYERS, Quasiconvexity and the semicontinuity of multiple variational integrals of any order. Trans. Amer. Math. Soc., Vol. 119, 1965, pp. 125-149.
12. C. B. MORREY, Quasiconvexity and the semicontinuity of multiple integrals. Pacific J. Math. 2, 1952, pp. 25-53.
13. C. B. MORREY, "Multiple integrals in the Calculus of Variations", 1966 (Berlin: Springer).
14. F. MURAT, A survey on Compensated Compactness. In "Contributions to modern calculus of variations. (ed.) L. Cesari. Pitman Research Notes in Mathematics Series 148, Longman, Harlow, 1987, pp. 145-183.
15. G. P. PARRY, On the planar rank-one convexity condition. Proc. Roy. Soc. Edinburgh, Vol. 125A, 1995, pp. 247-264.
16. P. PEDREGAL, Laminates and microstructure. Europ. J. Appl. Math., Vol. 4 (1993), 121-149.
17. P. PEDREGAL, Some remarks on quasiconvexity and rank-one convexity. preprint, 1995.
18. D. SERRE, Formes quadratiques et calcul des variations. J. Math. pures et appl., Vol. 62, 1983, pp. 177-196.
19. V. ŠVERÁK, Examples of rank-one convex functions, Proc. Roy. Soc. Edinburgh, Vol. 114A, 1990, pp. 237-242.
20. V. ŠVERÁK, Quasiconvex functions with subquadratic growth. Proc. Roy. Soc. London, Vol. 433A 1991, pp. 723-725.
21. V. ŠVERÁK, Rank-one convexity does not imply quasiconvexity, Proc. Roy. Soc. Edinburgh 120A, 1992, pp. 185-189.
22. L. TARTAR, The compensated compactness method applied to systems of conservation laws. In "Systems of Nonlinear Partial Differential Equations"; J. M. BALL (ed.), 1983 (D. Reidel Publ. Company), pp. 263-285.
23. L. TARTAR, On separately convex functions. In "Microstructure and Phase Transition" (eds.) D. KINDERLEHRER, R. JAMES, M. LUSKIN and J. L. ERICKSEN. The IMA volumes in mathematics and its applications, Vol. 54, 1993 (New York: Springer).
24. F. J. TEPSTRA, Die darstellung der biquadratischen formen als summen von quadraten mit anwendung auf die variationsrechnung. Math. Ann., Vol. 116, 1938, pp. 166-180.
25. K.-W. ZHANG, A construction of quasiconvex functions with linear growth at infinity. Ann. Sc. Norm. Sup. Pisa Serie IV, Vol. XIX, 1992, pp. 313-326.
26. K.-W. ZHANG, On various semiconvex hulls in the calculus of variations. preprint, 1996.
27. K.-W. ZHANG, On the structure of quasiconvex hulls, preprint, 1996.