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Referenza completa

Bousselsal, M. and Le Dret, H.:
Remarks on the quasiconvex envelope of some functions depending on quadratic forms
Bollettino dell'Unione Matematica Italiana Serie 8 5-B (2002), fasc. n.2, p. 469-486, Unione Matematica Italiana (English)
pdf (288 Kb), djvu (222 Kb). | MR1911201 | Zbl 1177.49009

Sunto

In questo lavoro calcoliamo la chiusura quasi convessa di alcune funzioni definite sullo spazio $M_{mn}$ delle matrici reali $m \times n$ attraverso forme quadratiche. I risultati sono applicati ad alcune funzioni relative alla densità di energia elastica di James e Ericksen.
Referenze Bibliografiche
[1] J. M. BALL, Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rational Mech. Anal., 64 (1977), 337-403. | MR 475169 | Zbl 0368.73040
[2] K. BHATTACHARYA-G. DOLZMAN, Relaxation of some multi-well problems, to appear, 1998. | MR 1830413 | Zbl 0977.74029
[3] M. BOUSSELSAL-B. BRIGHI, Rank-one-convex and quasiconvex envelopes for functions depending on quadratic forms, J. Convex Anal., 4 (1997), 305-319. | MR 1613479 | Zbl 0903.49011
[4] C. COLLINS-M. LUSKIN, Numerical modeling of the microstructure of crystals with symmetry-related variants, in Proceedings of the ARO US-Japan Workshop on Smart/Intelligent Materials and Systems, Honolulu, Hawaii, Technomic Publishing Company, Lancaster, PA, 1990.
[5] B. DACOROGNA, Direct Methods in the Calculus of Variations, Applied Mathematical Sciences, no. 78, Springer-Verlag, Berlin, 1989. | MR 990890 | Zbl 0703.49001
[6] R. V. KOHN-G. STRANG, Explicit relaxation of a variational problem in optimal design, Bull. A.M.S., 9 (1983), 211-214. | fulltext mini-dml | MR 707959 | Zbl 0527.49002
[7] R. V. KOHN-G. STRANG, Optimal design and relaxation of variational problems, I, II and III, Comm. Pure Appl. Math., 39 (1986), 113-137, 139-182 and 353-377. | MR 820342 | Zbl 0621.49008
[8] H. LE DRET-A. RAOULT, The quasiconvex envelope of the Saint Venant-Kirchhoff stored energy function, Proc. Roy. Soc. Edinburgh A, 125 (1995), 1179-1192. | MR 1362998 | Zbl 0843.73016
[9] H. LE DRET-A. RAOULT, Quasiconvex envelopes of stored energy densities that are convex with respect to the strain tensor, in Calculus of Variations, Applications and Computations, Pont-a-Mousson 1994 (C. Bandle, J. Bemelmans, M. Chipot, J. Saint Jean Paulin, I. Shafrir eds.), 138-146, Pitman Research Notes in Mathematics, Longman, 1995. | MR 1419340 | Zbl 0830.73012
[10] C. B. JR. MORREY, Quasiconvexity and the semicontinuity of multiple integrals, Pacific J. Math., 2 (1952), 25-53. | fulltext mini-dml | MR 54865 | Zbl 0046.10803
[11] C. B. JR. MORREY, Multiple Integrals in the Calculus of Variations, Springer-Verlag, Berlin, 1966. | MR 202511 | Zbl 0142.38701
[12] V. ŠVERÁK, Rank-one-convexity does not imply quasiconvexity, Proc. Royal Soc. Edinburgh A, 120 (1992), 185-189. | MR 1149994 | Zbl 0777.49015

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