Finding New Families of Rank-One Convex Polynomials
Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 5, p. 1621-1634
@article{AIHPC_2009__26_5_1621_0,
     author = {Bandeira, Lu\'\i S and Pedregal, Pablo},
     title = {Finding New Families of Rank-One Convex Polynomials},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {26},
     number = {5},
     year = {2009},
     pages = {1621-1634},
     doi = {10.1016/j.anihpc.2008.08.002},
     zbl = {pre05612920},
     mrnumber = {2566703},
     language = {en},
     url = {http://http://www.numdam.org/item/AIHPC_2009__26_5_1621_0}
}
Bandeira, LuíS; Pedregal, Pablo. Finding New Families of Rank-One Convex Polynomials. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 5, pp. 1621-1634. doi : 10.1016/j.anihpc.2008.08.002. http://www.numdam.org/item/AIHPC_2009__26_5_1621_0/

[1] Alibert J. J., Dacorogna B., An Example of a Quasiconvex Function Not Polyconvex in Dimension 2, Arch. Rational Mech. Anal. 117 (1992) 155-166. | MR 1145109 | Zbl 0761.26009

[2] Ball J. M., Convexity Conditions and Existence Theorems in Nonlinear Elasticity, Arch. Rational Mech. Anal. 63 (1977) 337-403. | MR 475169 | Zbl 0368.73040

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

[4] Dacorogna B., Douchet J., Gangbo W., Rappaz J., Some Examples of Rank One Convex Functions in Dimension Two, Proc. Roy. Soc. Edinburgh Sect. A 114 (1-2) (1990) 135-150. | MR 1051612 | Zbl 0722.49018

[5] Dacorogna B., Marcellini P., A Counterexample in the Vectorial Calculus of Variations, in: Material Instabilities in Continuum Mechanics, Oxford Sci. Publ., Oxford Univ. Press, New York, 1988, pp. 77-83. | MR 970519 | Zbl 0641.49007

[6] Gutiérrez S., A Necessary Condition for the Quasiconvexity of Polynomials of Degree Four, J. Convex Anal. 13 (1) (2006) 51-60. | MR 2211803 | Zbl 1115.49016

[7] Morrey C. B., Quasiconvexity and the Lower Semicontinuity of Multiple Integrals, Pacific J. Math. 2 (1952) 25-53. | MR 54865 | Zbl 0046.10803

[8] Pedregal P., Laminates and Microstructure, Eur. J. Appl. Math. 4 (2) (1993) 121-149. | MR 1228114 | Zbl 0779.73050

[9] Schost E., Computing Parametric Geometric Resolutions, Appl. Algebra Engrg. Comm. Comput. 13 (5) (2003) 349-393. | MR 1959170 | Zbl 1058.68123

[10] Wang D., Elimination Methods, Texts and Monographs in Symbolic Computation, Springer, 2001. | MR 1826878 | Zbl 0964.13014

[11] Weispfenning V., Comprehensive Gröbner Bases, J. Symbolic Comput. 14 (1992) 1-29. | MR 1177987 | Zbl 0784.13013