Quasiconvex functions, SO(n) and two elastic wells
Annales de l'I.H.P. Analyse non linéaire, Tome 14 (1997) no. 6, pp. 759-785. 
@article{AIHPC_1997__14_6_759_0,
     author = {Zhang, Kewei},
     title = {Quasiconvex functions, $SO(n)$ and two elastic wells},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {759--785},
     publisher = {Gauthier-Villars},
     volume = {14},
     number = {6},
     year = {1997},
     mrnumber = {1482901},
     zbl = {0918.49014},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPC_1997__14_6_759_0/}
}
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Zhang, Kewei. Quasiconvex functions, $SO(n)$ and two elastic wells. Annales de l'I.H.P. Analyse non linéaire, Tome 14 (1997) no. 6, pp. 759-785. http://archive.numdam.org/item/AIHPC_1997__14_6_759_0/

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

[Bd] E.J. Balder, A general approach to lower semicontinuity and lower closure in optimal control theory, SIAM J. Control and Optimization, Vol. 22, 1984, pp. 570-597. | MR | Zbl

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

[Bl1] J.M. Ball, Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rational Mech. Anal., Vol. 63, 1977, pp. 337-403. | MR | Zbl

[Bl2] J.M. Ball, Constitutive inequalities and existence theorems in nonlinear elasticity, in "Nonlinear Analysis and Mechanics: Heriot - Watt Symposium." Vol. 1 (edited by R. mJ. Knops), Pitman, London, 1977. | MR | Zbl

[Bl3] 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, 207-215, Springer-Verlag. | MR | Zbl

[BCO] J.M. Ball, J.C. Currie and P.J. Olver, Null Lagrangians, weak continuity, and variational problems of arbitrary order, J. Functional Anal., Vol. 41, 1981, pp. 135-174. | MR | Zbl

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

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

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

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

[Da1] B. Dacorogna, Weak Continuity and Weak Lower Semicontinuity of Nonlinear Functionals, Lectures Notes in Math., Springer-Verlag, Berlin, Vol. 922, 1980. | MR | Zbl

[Da2] B. Dacorogna, Direct Methods in the Calculus of Variations, Springer, 1989. | MR | Zbl

[DR] H. Le Dret and A. Raoult, Enveloppe quasi-convexe de la densité d'énergie de Saint Venant-Kirchhoff, C. R. Acad. Sci. Paris, Série I, Vol. 318, 1994, pp. 93-98. | MR | Zbl

[ET] I. Ekeland and R. Temam, Convex Aanlysis and Variational Problems, North-Holland, 976. | Zbl

[F] I. Fonseca, The lower quasiconvex envelope of the stored energy function for an elastic crystal, J. Math. Pures et Appl., Vol. 67, 1988, pp. 175-195. | MR | Zbl

[K] R.V. Kohn, The relaxation of a double-well energy, Cont. Mech. Therm., Vol. 3, 1991, pp. 981-1000. | MR | Zbl

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

[KS] R.V. Kohn and D. Strang, Optimal design and relaxation of variational problems I, II, III, Comm. Pure Appl. Math., Vol. 39, 1986, pp. 113-137, 139-182, 353-377. | MR | Zbl

[L] F.C. Liu, A Luzin type property of Sobolev functions, Ind. Univ. Math. J., Vol. 26, 1977, pp. 645-651. | MR | Zbl

[Ma] J. Matos, Young measures and the absence of fine microstructures in the α - β quarts phase transition, preprint.

[Mo] C.B. Jr Morrey, Multiple integrals in the calculus of variations, Springer, 1966. | MR | Zbl

[Sv] V. Sverák, On the problem of two wells, preprint. | MR

[St] E.M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton , 1970. | MR | Zbl

[T] L. Tartar, Compensated compactness and applications to partial differential equations, Nonlinear Analysis and Mechanics: Heriot-Watt Symposium (edited by R. J. Knops) Vol. IV, 1979, pp. 136-212. | MR | Zbl

[Z] 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 | Zbl