no. 5
On the definition and the lower semicontinuity of certain quasiconvex integrals
Annales de l'I.H.P. Analyse non linéaire, Tome 3 (1986) no. 5, pp. 391-409. 
@article{AIHPC_1986__3_5_391_0,
     author = {Marcellini, Paolo},
     title = {On the definition and the lower semicontinuity of certain quasiconvex integrals},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {391--409},
     publisher = {Gauthier-Villars},
     volume = {3},
     number = {5},
     year = {1986},
     mrnumber = {868523},
     zbl = {0609.49009},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_1986__3_5_391_0/}
}
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Marcellini, Paolo. On the definition and the lower semicontinuity of certain quasiconvex integrals. Annales de l'I.H.P. Analyse non linéaire, Tome 3 (1986) no. 5, pp. 391-409. http://www.numdam.org/item/AIHPC_1986__3_5_391_0/

[1] E. Acerbi, N. Fusco, Semicontinuity problems in the calculus of variations, Arch. Rat. Mech. Anal., t. 86, 1984, p. 125-145. | MR | Zbl

[2] S.S. Antman, The influence of elasticity on analysis: modern developments, Bull. Amer. Math. Soc., t. 9, 1983, p. 267-291. | MR | Zbl

[3] J.M. Ball, Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rat. Mech. Anal., t. 63, 1977, p. 337-403. | MR | Zbl

[4] J.M. Ball, Discontinuous equilibrium solutions and cavitation in nonlinear elasticity, Phil. Trans. R. Soc. Lond., t. 306, 1982, p. 557-611. | MR | Zbl

[5] J.M. Ball, F. Murat, W1,p-quasiconvexity and variational problems for multiple integrals, J. Functional Analysis, t. 58, 1984, p. 225-253. | MR | Zbl

[6] B. Dacorogna, Weak continuity and weak lower semicontinuity of nonlinear functionals, Lecture Notes in Math., t. 922, 1982, Springer-Verlag, Berlin. | MR | Zbl

[7] G. Dal Maso, Integral representation on BV(Ω) of Γ-limits of variational integrals, Manuscripta Math., t. 30, 1980, p. 387-416. | MR | Zbl

[8] E. De Giorgi, Teoremi di semicontinuità nel calcolo delle variazioni, Istituto Nazionale di Alta Matematica, Roma, 1968-1969.

[9] E. De Giorgi, Sulla convergenza di alcune successioni di integrali del tipo dell'area, Rendiconti Mat., t. 8, 1975, p. 277-294. | MR | Zbl

[10] C.L. Evans, Quasiconvexity and partial regularity in the calculus of variations, preprint.

[11] F. Ferro, Functionals defined on functions of bounded variation in Rn and the Lebesgue area, SIA M J. Control Optimization, t. 16, 1978, p. 778-789. | MR | Zbl

[12] M. Giaquinta, G. Modica, J. Soucek, Functionals with linear growth in the calculus of variations I, Commentationes Math. Univ. Carolinae, t. 20, 1979, p. 143-172. | MR | Zbl

[13] M. Giaquinta, G. Modica, Partial regularity of minimizers of quasiconvex integrals, Ann. Inst. H. Poincaré, Analyse non linéaire, to appear. | Numdam | MR | Zbl

[14] E. Giusti, Non-parametric minimal surfaces with discontinuous and thin obstacles, Arch. Rat. Mech. Anal., t. 49, 1972, p. 41-56. | MR | Zbl

[15] R.J. Knops, C.A. Stuart, Quasiconvexity and uniqueness of equilibrium solutions in nonlinear elasticity, Arch. Rat. Mech. Anal., t. 86, 1984, p. 233-249. | MR | Zbl

[16] R.V. Kohn, G. Strang, Optimal design and relaxation of variational problems, preprint.

[17] H. Lebesgue, Intégrale, longueur, aire, Ann. Mat. Pura Appl., t. 7, 1902, p. 231-359. | JFM

[18] P. Marcellini, Quasiconvex quadratic forms in two dimensions, Appl. Math. Optimization, t. 11, 1984, p. 183-189. | MR | Zbl

[19] P. Marcellini, Approximation of quasiconvex functions, and lower semicontinuity of multiple integrals, Manuscripta Math., t. 51, 1985, p. 1-28. | MR | Zbl

[20] P. Marcellini, C. Sbordone, On the existence of minima of multiple integrals of the calculus of variations, J. Math. Pures Appl., t. 62, 1983, p. 1-9. | MR | Zbl

[21] N. Meyers, Quasiconvexity and lower semicontinuity of multiple integrals of any order, Trans. Amer. Math. Soc., t. 119, 1965, p. 125-149. | MR | Zbl

[22] M. Miranda. Un teorema di esistenza e unicità per il problema dell'area minima in n variabili, Ann. Scuola Norm. Sup. Pisa, t. 19. 1965, p. 233-249. | Numdam | MR | Zbl

[23] C.B. Morrey, Multiple integrals in the calculus of variations, 1966, Springer-Verlag, Berlin. | MR | Zbl

[24] J. Serrin, On the definition and properties of certain variational integrals, Trans. Amer. Math. Soc., t. 101. 1961, p. 139-167. | MR | Zbl