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Fourth-order moments of nonnegative measures on S2 and applications

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References

  1. Artstein, Z., Look for the Extreme Points, SIAM Review 22, 1980, 172–185.

    Google Scholar 

  2. Avellaneda, M., Optimal Bounds and Microgeometries for Elastic Two-phase Composites, SIAM J. Appl. Math. 47, 1987, 1216–1228.

    Google Scholar 

  3. Allaire, G. & Kohn, R. V., Optimal Bounds on the Effective Behaviour of a Mixture of Two Well Ordered Elastic Materials, Quart. Appl. Math. 51, 1993, 643–674.

    Google Scholar 

  4. Avellaneda, M. & Milton, G. W., Bounds on the Effective Elasticity Tensor of Composites Based on Two Point Correlations, in Proceedings of the ASME Energy Technology Conference and Exposition, Houston, 1989, eds. Hui, D. & Kozic, T., ASME Press, New York, 1989.

    Google Scholar 

  5. Choi, M. D. & Lam, T. Y., An Old Question of Hubert, Queens Papers on Pure and Applied Math., Queens University, Kingston, Ontario, 1977.

    Google Scholar 

  6. Crouzeix, M. & Mignot, A. L., Analyse numérique des équations différentielles, Masson, Paris, 1984.

    Google Scholar 

  7. Dal Maso, G. & Kohn, R. V., The Local Character of G-closure, to appear.

  8. Francfort, G. A. & Marigo, J. J., Stable Damage Evolution in a Brittle Continuous Medium, Eur. J. Mech. A./Solids 12, 1993, 149–189.

    Google Scholar 

  9. Francfort, G. A. & Murat, F., Homogenization and Optimal Bounds in Linear Elasticity, Arch. Rational Mech. Anal. 94, 1986, 307–334.

    Google Scholar 

  10. Hashin, Z., Analysis of Composite Materials, a Survey, J. Appl. Mech., Trans. ASME 105, 1983, 481–505.

    Google Scholar 

  11. Hilbert, D., Über die Darstellung definiter Formen als Summe von Formenquadraten, Math. Ann. 32, 1888, 342–350.

    Google Scholar 

  12. Hashin, Z., & Shtrikman, S., A Variational Approach to the Theory of the Elastic Behaviour of Multiphase Materials, J. Mech. Phys. Solids 11, 1963, 127–140.

    Google Scholar 

  13. Lipton, R., On the Behaviour of Elastic Composites with Transverse Isotropy Symmetry, J. Mech. Phys. Solids 39, 1991, 663–681.

    Google Scholar 

  14. Milton, G. W., On Characterizing the Set of Possible Effective Tensors of Composites: The Variational Method and the Translation Method, Comm. Pure Appl. Math. 43, 1990, 63–125.

    Google Scholar 

  15. Motzkin, T. S., The Arithmetic-Geometric Inequality, in Inequalities, ed. Shisha, O., Academic Press, New York, 1967, 205–224.

    Google Scholar 

  16. Milton, G. W. & Kohn, R. V., Variational Bounds on the Effective Moduli of Anisotropic Composites, J. Mech. Phys. Solids 36, 1988, 597–629.

    Google Scholar 

  17. Murat, F. & Tartar, L., H-convergence, in Topics in the Mathematical Modelling of Composite Materials, ed. R. V. Kohn, Birkhaüser, Boston, to appear.

  18. Tartar L., Cours Peccot, 1977, Collège de France, Paris; partially written in [MT].

    Google Scholar 

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Communicated by J. Ball

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Francfort, G., Murat, F. & Tartar, L. Fourth-order moments of nonnegative measures on S2 and applications. Arch. Rational Mech. Anal. 131, 305–333 (1995). https://doi.org/10.1007/BF00380913

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