Quasiconvex functions, $SO\left(n\right)$ and two elastic wells

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1. [AF] E. Acerbi and N. Fusco, Semicontinuity problems in the calculus of variations, Arch. Rational Mech. Anal., Vol. 86, 1984, pp. 125-145. Zbl0565.49010MR751305
2. [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. Zbl0549.49005MR747970
3. [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. Zbl0282.49041MR344980
4. [Bl1] J.M. Ball, Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rational Mech. Anal., Vol. 63, 1977, pp. 337-403. Zbl0368.73040MR475169
5. [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. Zbl0377.73043MR478899
6. [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. Zbl0991.49500MR1036070
7. [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. Zbl0459.35020MR615159
8. [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 Zbl0808.73063MR1303758
9. [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. Zbl0629.49020MR906132
10. [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. Zbl0758.73009
11. [CK] M. Chipot and D. Kinderlehrer, Equilibrium configurations of crystals, Arch. Rational Mech. Anal., Vol. 103, 1988, pp. 237-277. Zbl0673.73012MR955934
12. [Da1] B. Dacorogna, Weak Continuity and Weak Lower Semicontinuity of Nonlinear Functionals, Lectures Notes in Math., Springer-Verlag, Berlin, Vol. 922, 1980. Zbl0676.46035MR658130
13. [Da2] B. Dacorogna, Direct Methods in the Calculus of Variations, Springer, 1989. Zbl0703.49001MR990890
14. [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. Zbl0792.73034MR1260543
15. [ET] I. Ekeland and R. Temam, Convex Aanlysis and Variational Problems, North-Holland, 976. Zbl0322.90046
16. [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. Zbl0718.73075MR949107
17. [K] R.V. Kohn, The relaxation of a double-well energy, Cont. Mech. Therm., Vol. 3, 1991, pp. 981-1000. Zbl0825.73029MR1122017
18. [KP] D. Kinderlehrer and P. Pedregal, Characterizations of Young measures generated by gradients, Arch. Rational Mech. Anal., Vol. 115, 1991, pp. 329-365. Zbl0754.49020MR1120852
19. [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. Zbl0609.49008MR820342
20. [L] F.C. Liu, A Luzin type property of Sobolev functions, Ind. Univ. Math. J., Vol. 26, 1977, pp. 645-651. Zbl0368.46036MR450488
21. [Ma] J. Matos, Young measures and the absence of fine microstructures in the α — β quarts phase transition, preprint. 
22. [Mo] C.B. Jr Morrey, Multiple integrals in the calculus of variations, Springer, 1966. Zbl0142.38701MR202511
23. [Sv] V. Sverák, On the problem of two wells, preprint. MR1320537
24. [St] E.M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton , 1970. Zbl0207.13501MR290095
25. [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. Zbl0437.35004MR584398
26. [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. Zbl0778.49015MR1205403

1. Kewei Zhang, An approximation theorem for sequences of linear strains and its applications
2. Kewei Zhang, An approximation theorem for sequences of linear strains and its applications