On the structure of quasiconvex hulls
Annales de l'I.H.P. Analyse non linéaire, Volume 15 (1998) no. 6, p. 663-686
@article{AIHPC_1998__15_6_663_0,
author = {Zhang, Kewei},
title = {On the structure of quasiconvex hulls},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
publisher = {Gauthier-Villars},
volume = {15},
number = {6},
year = {1998},
pages = {663-686},
zbl = {0917.49014},
mrnumber = {1650974},
language = {en},
url = {http://www.numdam.org/item/AIHPC_1998__15_6_663_0}
}

Zhang, Kewei. On the structure of quasiconvex hulls. Annales de l'I.H.P. Analyse non linéaire, Volume 15 (1998) no. 6, pp. 663-686. http://www.numdam.org/item/AIHPC_1998__15_6_663_0/

[A] E.M. Alfsen, Compact Convex Sets and Boundary Integrals, Springer-Verlag, 1971. | MR 445271 | Zbl 0209.42601

[AF] E. Acerbi and N. Fusco, Semicontinuity problems in the calculus of variations. Arch. Rational Mech. Anal., Vol. 86, 1984, pp. 125-145. | MR 751305 | Zbl 0565.49010

[BL] H. Berliocchi, J.M. Lasry, Intégrandes normales et mesures paramétrées en calcul des variations. Bull. Soc. Math. France, Vol. 101, 1973, pp. 129-184. | Numdam | MR 344980 | Zbl 0282.49041

[B11] J.M. Ball, Convexity conditions and existence theorems in nonlinear elasticity. Arch. Rational Mech. Anal., Vol. 63, 1977, pp. 337-403. | MR 475169 | Zbl 0368.73040

[B12] J.M. Ball, A version of the fundamental theorem of Young measures, in Partial Differential Equations and Continuum Models of Phase Transitions, (edited by M. RASCLE, D. SERRE and M. SLEMROD), 1989, pp. 207-215, Springer-Verlag. | MR 1036070 | Zbl 0991.49500

[B13] J.M. Ball, Sets of gradients with no rank-one connections. J. Math. Pures et Appl., Vol. 69, 1990, pp. 241-259. | MR 1070479 | Zbl 0644.49011

[BFJK] K. Bhattacharya, N.B. Firoozye, R.D. James, R.V. Kohn, Restrictions on Microstructures. Proc. Royal Soc. Edinburgh, A, Vol. 124, 1994, pp. 843-878. | MR 1303758 | Zbl 0808.73063

[BJ1] J.M. Ball, R.D. James, Fine phase mixtures as minimizers of energy. Arch. Rational Mech. Anal., Vol. 100, 1987, pp. 13-52. | MR 906132 | Zbl 0629.49020

[BJ2] J.M. Ball, R.D. James, Proposed experimental tests of a theory of fine microstructures and the two-well problem. Phil. Roval Soc. Lon., Vol. 338A, 1992, pp. 389-450. | Zbl 0758.73009

[BZ] J.M. Ball and K.-W. Zhang, Lower semicontinuity and multiple integrals and the biting lemma . Proc. Royal Soc. Edinburgh, Vol. 114A, 1990, pp. 367-379. | MR 1055554 | Zbl 0716.49011

[CK] M. Chipot, D. Kinderlehrer, Equilibrium configurations of crystals Arch. Rational Mech. Anal., Vol. 103, 1988, pp. 237-277. | MR 955934 | Zbl 0673.73012

[D] B. Dacorogna, Direct Methods in the Calculus of Variations, Springer-Verlag, 1989. | MR 990890 | Zbl 0703.49001

[ET] I. Ekeland, R. Temam, Convex Aanlysis and Variational Problems, North-Holland, 1976. | MR 463994 | Zbl 0322.90046

[K] D. Kinderlehrer, Remarks about equilibrium configurations of crystals, in Material Instabilities in Continuum Mechanics, J. M. BALL ed., Oxford University Press, 1988, pp. 977-83. | MR 970527 | Zbl 0850.73037

[KP] D. Kinderlehrer, P. Pedregal, Characterizations of Young measures generated by gradients. Arch. Rational Mech. Anal, Vol. 115, 1991, pp. 329-365. | MR 1120852 | Zbl 0754.49020

[Ma] J.P. Matos, Young measures and the absence of fine microstructures in a class of phase transitions. European J. Appl. Math, Vol. 3, 1992, pp. 31-54. | MR 1156593 | Zbl 0751.73003

[Mo] C.B. Jrmorrey, Multiple integrals in the calculus of variations, Springer, 1966. | MR 202511 | Zbl 0142.38701

[MS] S. Müller, V. Šverák, Attainment results for the two-well problem by convex integration, preprint, 1993.

[Re] Yu.G. Reshetnak, Liouville's theorem on conformal mappings under minimal regularity assumptions. Siberian Math. J., Vol. 8, 1967, pp. 631-653. | Zbl 0167.36102

[Ro] R.T. Rockafellar, Convex Analysis, Princeton University Press, 1970. | MR 274683 | Zbl 0193.18401

[Ru] W. Rudin, Functional Analysis, McGraw-Hill, 1973. | MR 365062 | Zbl 0253.46001

[Sv1] V. Šverák, On the problem of two wells, preprint. | MR 1320537

[Sv2] V. Šverák, On Tartar's conjecture. Ann. Inst. H. Poincaré, Vol. 10, 1993, pp. 405-412. | Numdam | MR 1246459 | Zbl 0820.35022

[Sv3] V. Šverák, Rank one convexity does not imply quasiconvexity. Proc. Royal Soc. Edin., Vol. 120A, 1992, pp. 185-189. | MR 1149994 | Zbl 0777.49015

[T] L. Tartar, Compensated compactness and applications to partial differential equations, in Nonlinear Analysis and Mechanics: Heriot-Watt Symposium, IV, R. J. Knops ed Pitman, 1979. | MR 584398 | Zbl 0437.35004

[Y] B.-S. Yan, Remarks on the set of quasi-conformal matrices in higher dimensions, Preprint, 1994.

[Z1] 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. | Numdam | MR 1205403 | Zbl 0778.49015

[Z2] K.-W. Zhang, On non-negative quasiconvex functions with unbounded zero sets, Proc. Royal Soc. Edin., Vol. 127A, 1997, pp. 411-422. | MR 1447961 | Zbl 0883.49013

[Z3] K.-W. Zhang, On some quasiconvex functions with linear growth, to appear in J. Convex Anal. | MR 1649465 | Zbl 0915.49008