Kinderlehrer, David; Pedregal, Pablo Characterizations of Young measures generated by gradients. (English) Zbl 0754.49020 Arch. Ration. Mech. Anal. 115, No. 4, 329-365 (1991). Il s’agit d’utiliser les méthodes variationelles pour étudier les configurations d’équilibre des solides cristallins. Pour cela la recherche présenté a comme point de départ la théorie de la thermoélasticité, qui a été l’objet de nombreuses publications récentes de J. L. Ericksen. Dans ce travail il est question des mesures paramétrisés ou mesures de Young, et avant tout on recherche quelles mesures ordinaires avec support en ensembles compactes de matrices peuvent dériver de limites de successions de gradients. Les auteurs donnent deux caractérisations, qui expriment la validité de l’inégalité de Jensen pour des classes de fonctions quasiconvexes (selon C. B. Morrey), l’une dans la classe des fonctions quasiconvexes qui sont identiquement \(+\infty\) au dehors d’une balle l’autre dans celle des fonctions quasiconvexes continues. Reviewer: S.Cinquini (Pavia) Cited in 3 ReviewsCited in 142 Documents MSC: 90C52 Methods of reduced gradient type Keywords:Young measures; equilibrium configurations of crystalline solids × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Acerbi, E. & Fusco, N., 1984, Semicontinuity problems in the calculus of variations. Arch. Rational Mech. Anal., 86, 125-145. · Zbl 0565.49010 · doi:10.1007/BF00275731 [2] Balder, E. J., 1984, A general approach to lower semicontinuity and lower closure in optimal control theory, SIAM J. Control Opt., 22, 570-597. · Zbl 0549.49005 · doi:10.1137/0322035 [3] Ball, J. M., 1984, Singular minimizers and their significance in elasticity, Phase Transformations and Material Instabilities in Solids, (Gurtin, M., ed.) Academic Press, 1-20. [4] Ball, J. 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