Implications of rank one convexity

 Access to full text

 Full (PDF)

1. [1] J.M. Ball, 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. Zbl0377.73043MR478899
2. [2] J.M. Ball, Convexity Conditions and Existence Theorems in Nonlinear Elasticity, Arch. Rat. Mech. Anal., Vol. 63, 1977, pp. 337-403. Zbl0368.73040MR475169
3. [3] J.M. Ball, 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. Zbl0613.49014
4. [4] J.M. Ball, J.C. Currie and P.J. Olver, Null Lagrangians, Weak Continuity and Variational Problems of Arbitrary Order, J. Funct. Anal., 41, 1981, pp. 135-174. Zbl0459.35020MR615159
5. [5] J.M. Ball and J.E. Marsden, Quasiconvexity at the Boundary, Positivity of the Second Variation and Elastic Stability, Arch. Rat. Mech. Anal., Vol. 86, 1984, pp. 251- 277. Zbl0552.73006MR751509
6. [6] L. Cesari, Optimization-Theory and Applications, Springer-Verlag, New York, 1983. Zbl0506.49001MR688142
7. [7] D.G.B. Edelen, The Null Set of the Euler-Lagrange Operator, Arch. Rat. Mech. Anal., 11, 1962, pp. 117-121. Zbl0125.33002MR150623
8. [8] J.L. Ericksen, Nilpotent Energies in Liquid Crystal Theory, Arch. Rat. Mech. Anal., 10, 1962, pp. 189-196. Zbl0109.23002MR169513
9. [9] R.J. Knops and C.A. Stuart, Quasiconvexity and Uniqueness of Equilibrium Solutions in Nonlinear Elasticity, Arch. Rat. Mech. Anal., Vol. 86, 1984, pp. 233- 249. Zbl0589.73017MR751508
10. [10] A.W. Landers, 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. Zbl0063.03441MR6821
11. [11] C.B. Morrey, Multiple Integrals in the Calculus of Variations, Springer, Berlin, 1966. Zbl0142.38701
12. [12] P.J. Olver, Conservation Laws and Null Divergences, Math. Proc. Cambridge Phil. Soc., 94, 1983, pp. 529-540. Zbl0556.35021MR720804
13. [13] P.J. Olver and J. Sivaloganathan, The Structure of Null Lagrangians, to appear in Nonlinearity. Zbl0662.49016MR937008
14. [14] H. Rund, The Hamilton-Jacobi Theory in the Calculus of Variations, Van Nostrand, London, 1966. Zbl0141.10602MR230189
15. [15] J. Sivaloganathan, A Field Theory Approach to Stability of Equilibria in Radial Elasticity, Math. Proc. Camb. Phil. Soc., 99, 1986, pp. 589-604. Zbl0612.73013MR830370
16. [16] C. Truesdell and W. Noll, The Nonlinear Field Theories of Mechnics, in Handbuch der Physik, Vol. III/3, S. FLUGGE Ed., Springer, Berlin, 1965. MR193816
17. [17] H. Weyl, Geodesic Fields, Ann. of Math., 37, 1935, pp. 607-629. Zbl0013.12002JFM61.0554.04

1. Krzysztof Chełmiński, Agnieszka Kałamajska, New convexity conditions in the calculus of variations and compensated compactness theory
2. Krzysztof Chełmiński, Agnieszka Kałamajska, New convexity conditions in the calculus of variations and compensated compactness theory