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Homogenization of nonconvex integral functionals and cellular elastic materials

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References

  • H. Attouch [1981]. Sur la Γ-convergence, in: H. Brézis and J. L. Lions (Eds.), Nonlinear partial differential equations and their applications. Collège de France Seminar, Vol. I, p. 7–41, Pitman, London.

    Google Scholar 

  • H. Attouch [1984]. Variational convergence for functions and operators, Pitman, London.

    Google Scholar 

  • J. M. Ball [1977]. Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rational Mech. Anal., 63, 337–403.

    Google Scholar 

  • J. M. Ball & F. Murat [1984]. W1,p-quasiconvexity and variational problems for multiple integrals, J. Funct. Anal., 58, 225–253.

    Google Scholar 

  • A. Bensoussan, J. L. Lions & G. Papanicolaou [1978]. Asymptotic analysis for periodic structures, North-Holland, Amsterdam.

    Google Scholar 

  • A. Braides [1985]. Homogenization of some almost periodic coercive functional, Rend. Accad. Naz. Sci. XL, 103, 313–322.

    Google Scholar 

  • L. Carbone & C. Sbordone [1979]. Some properties of Γ-limits of integral functionals, Annali Mat. Pura Appl., 122, 1–60.

    Google Scholar 

  • D. Cioranescu & J. Saint Jean Paulin [1979]. Homogenization in open sets with holes, J. Math. Anal. Appl., 71, 590–607.

    Google Scholar 

  • G. Dal Maso & L. Modica [1981]. A general theory of variational functionals, in: Topics in functional analysis 1980–81, by F. Strocchi, E. Zarantonello, E. De Giorgi, G. Dal Maso, L. Modica, Scuola Normale Superiore, Pisa, p. 149–221.

    Google Scholar 

  • I. Ekeland & R. Temam [1974]. Analyse convexe et problèmes variationnels, Dunod, Gauthier-Villars.

    Google Scholar 

  • N. Fusco [1983]. On the convergence of integral functionals depending on vector-valued functions, preprint no. 102, Univ. Napoli.

  • L. J. Gibson & M. F. Ashby [1982]. The mechanics of three-dimensional cellular materials, Proc. R. Soc. Lond., A 382, 43–59.

    Google Scholar 

  • E. De Giorgi [1975]. Sulla convergenza di alcune successioni d'integrali del tipo dell' area, Rend. Matsmatica, 8, 277–294.

    Google Scholar 

  • E. De Giorgi [1979]. Convergence problems for functions and operators, Proc. Int. Meeting on “Recent methods in nonlinear analysis”, Rene 1978, ed. E. De Giorgi, E. Magenes, Mosco Pitagora, Bologna, p. 131–188.

    Google Scholar 

  • E. De Giorgi & G. Dal Maso [1983]. Γ-convergence and calculus of variations. In: J. P. Cecconi and T. Zolezzi (Eds.), Mathematical theories of optimization, Lecture Notes Maths. 979, Springer, Berlin, Heidelberg, New York.

  • E. De Giorgi & T. Franzoni [1975]. Su un tipo di convergenza variazionale, Atti. Accad. Naz. Lincei, Rend. Cl. Sc. Mat. (8), 58, 842–850.

    Google Scholar 

  • A. N. Gent & A.G. Thomas [1959]. The deformation of foamed elastic materials, J. Appl. Polym. Sci., 1, 107–113.

    Google Scholar 

  • D. Gilbarg & N. S. Trudinger [1983]. Elliptic partial differential equations of second order, 2nd edition, Springer, Berlin, Heidelberg, New York.

    Google Scholar 

  • N. C. Hilyard (Ed.) [1982]. Mechanics of cellular plastics, Applied Science Publ., London.

    Google Scholar 

  • P. Marcellini [1978]. Periodic solutions and homogenization of nonlinear variational problems, Annali Mat. Pura Appl. 117, 139–152.

    Google Scholar 

  • Yu. G. Reshetnyak [1967]. On the stability of conformal mappings in multidimensional spaces, Siberian Math. J., 8, 69–85.

    Google Scholar 

  • E. Sanchez-Palencia [1980]. Nonhomogeneous media and vibration theory, Lecture Notes in Physics, 127, Springer, Berlin, Heidelberg, New York.

  • I. Tartar [1977]. Cours Peccot au Collège de France, Paris.

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Communicated by G. Strang

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Müller, S. Homogenization of nonconvex integral functionals and cellular elastic materials. Arch. Rational Mech. Anal. 99, 189–212 (1987). https://doi.org/10.1007/BF00284506

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