@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}, volume = {14}, year = {1997}, pages = {759-785}, mrnumber = {1482901}, zbl = {0918.49014}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPC_1997__14_6_759_0} }
Zhang, Kewei. Quasiconvex functions, $SO(n)$ and two elastic wells. Annales de l'I.H.P. Analyse non linéaire, Tome 14 (1997) pp. 759-785. http://gdmltest.u-ga.fr/item/AIHPC_1997__14_6_759_0/
[AF] Semicontinuity problems in the calculus of variations, Arch. Rational Mech. Anal., Vol. 86, 1984, pp. 125-145. | MR 751305 | Zbl 0565.49010
and ,[Bd] 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 747970 | Zbl 0549.49005
,[BL] Intégrandes normales et mesures paramétrées en calcul des variations, Bull. Soc. Math. France, Vol. 101, pp. 129-184. | Numdam | MR 344980 | Zbl 0282.49041
and ,[Bl1] Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rational Mech. Anal., Vol. 63, 1977, pp. 337-403. | MR 475169 | Zbl 0368.73040
,[Bl2] 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 478899 | Zbl 0377.73043
,[Bl3] 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 1036070 | Zbl 0991.49500
,[BCO] Null Lagrangians, weak continuity, and variational problems of arbitrary order, J. Functional Anal., Vol. 41, 1981, pp. 135-174. | MR 615159 | Zbl 0459.35020
, and ,[BFJK] Restrictions on Microstructures, Proc. Royal Soc. Edinburgh A Vol. 124, 1994, pp. 843-878 | MR 1303758 | Zbl 0808.73063
, , and ,[BJ1] Fine phase mixtures as minimizers of energy, Arch. Rational Mech. Anal., Vol. 100, 1987, pp. 13-52. | MR 906132 | Zbl 0629.49020
and ,[BJ2] 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 0758.73009
and ;[CK] Equilibrium configurations of crystals, Arch. Rational Mech. Anal., Vol. 103, 1988, pp. 237-277. | MR 955934 | Zbl 0673.73012
and ,[Da1] Weak Continuity and Weak Lower Semicontinuity of Nonlinear Functionals, Lectures Notes in Math., Springer-Verlag, Berlin, Vol. 922, 1980. | MR 658130 | Zbl 0676.46035
,[Da2] Direct Methods in the Calculus of Variations, Springer, 1989. | MR 990890 | Zbl 0703.49001
,[DR] 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 1260543 | Zbl 0792.73034
and ,[ET] Convex Aanlysis and Variational Problems, North-Holland, 976. | Zbl 0322.90046
and ,[F] 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 949107 | Zbl 0718.73075
,[K] The relaxation of a double-well energy, Cont. Mech. Therm., Vol. 3, 1991, pp. 981-1000. | MR 1122017 | Zbl 0825.73029
,[KP] Characterizations of Young measures generated by gradients, Arch. Rational Mech. Anal., Vol. 115, 1991, pp. 329-365. | MR 1120852 | Zbl 0754.49020
and ,[KS] 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 820342 | Zbl 0609.49008
and ,[L] A Luzin type property of Sobolev functions, Ind. Univ. Math. J., Vol. 26, 1977, pp. 645-651. | MR 450488 | Zbl 0368.46036
,[Ma] Young measures and the absence of fine microstructures in the α - β quarts phase transition, preprint.
,[Mo] Multiple integrals in the calculus of variations, Springer, 1966. | MR 202511 | Zbl 0142.38701
,[Sv] On the problem of two wells, preprint. | MR 1320537
,[St] Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton , 1970. | MR 290095 | Zbl 0207.13501
,[T] 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 584398 | Zbl 0437.35004
,[Z] 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
,