@article{AIHPC_1988__5_2_99_0,
author = {Sivaloganathan, J.},
title = {Implications of rank one convexity},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
volume = {5},
year = {1988},
pages = {99-118},
mrnumber = {954467},
zbl = {0664.73006},
language = {en},
url = {http://dml.mathdoc.fr/item/AIHPC_1988__5_2_99_0}
}
Sivaloganathan, J. Implications of rank one convexity. Annales de l'I.H.P. Analyse non linéaire, Tome 5 (1988) pp. 99-118. http://gdmltest.u-ga.fr/item/AIHPC_1988__5_2_99_0/
[1] , Constitutive Inequalities and Existence Theorems in Nonlinear Elastostatics, in Nonlinear Analysis and Mechanics: Heriot-Watt Symposium, Vol. 1, R. J. KNOPS Ed., 1977, pp. 187-241, Pitman, London. | MR 478899 | Zbl 0377.73043
[2] , Convexity Conditions and Existence Theorems in Nonlinear Elasticity, Arch. Rat. Mech. Anal., Vol. 63, 1977, pp. 337-403. | MR 475169 | Zbl 0368.73040
[3] , Does Rank-One Convexity Imply Quasiconvexity? Proceedings of Workshop on Metastability and Partial Differential Equations, Institute for Mathematics and its Applications, University of Minnesota, May 1985. | Zbl 0613.49014
[4] , and , Null Lagrangians, Weak Continuity and Variational Problems of Arbitrary Order, J. Funct. Anal., 41, 1981, pp. 135-174. | MR 615159 | Zbl 0459.35020
[5] and , Quasiconvexity at the Boundary, Positivity of the Second Variation and Elastic Stability, Arch. Rat. Mech. Anal., Vol. 86, 1984, pp. 251- 277. | MR 751509 | Zbl 0552.73006
[6] , Optimization-Theory and Applications, Springer-Verlag, New York, 1983. | MR 688142 | Zbl 0506.49001
[7] , The Null Set of the Euler-Lagrange Operator, Arch. Rat. Mech. Anal., 11, 1962, pp. 117-121. | MR 150623 | Zbl 0125.33002
[8] , Nilpotent Energies in Liquid Crystal Theory, Arch. Rat. Mech. Anal., 10, 1962, pp. 189-196. | MR 169513 | Zbl 0109.23002
[9] and , Quasiconvexity and Uniqueness of Equilibrium Solutions in Nonlinear Elasticity, Arch. Rat. Mech. Anal., Vol. 86, 1984, pp. 233- 249. | MR 751508 | Zbl 0589.73017
[10] , Invariant Multiple Integrals in the Calculus of Variations, in Contributions to the Calculus of Variations, 1938-1941, pp. 175-208, Univ. Chicago Press, Chicago, 1942. | MR 6821 | Zbl 0063.03441
[11] , Multiple Integrals in the Calculus of Variations, Springer, Berlin, 1966. | Zbl 0142.38701
[12] , Conservation Laws and Null Divergences, Math. Proc. Cambridge Phil. Soc., 94, 1983, pp. 529-540. | MR 720804 | Zbl 0556.35021
[13] and , The Structure of Null Lagrangians, to appear in Nonlinearity. | MR 937008 | Zbl 0662.49016
[14] , The Hamilton-Jacobi Theory in the Calculus of Variations, Van Nostrand, London, 1966. | MR 230189 | Zbl 0141.10602
[15] , A Field Theory Approach to Stability of Equilibria in Radial Elasticity, Math. Proc. Camb. Phil. Soc., 99, 1986, pp. 589-604. | MR 830370 | Zbl 0612.73013
[16] and , The Nonlinear Field Theories of Mechnics, in Handbuch der Physik, Vol. III/3, S. FLUGGE Ed., Springer, Berlin, 1965. | MR 193816
[17] , Geodesic Fields, Ann. of Math., 37, 1935, pp. 607-629. | JFM 61.0554.04 | Zbl 0013.12002