On the compactness of minimizing sequences of variational problems

Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 979)


Lower Semicontinuity Quasiconformal Mapping Regularity Result Liouville Theorem Liouville Type Theorem 
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  1. [1]
    E.ACERBI-N.FUSCO, Semicontinuity problems in the Calculus of Variations, Arch. Rational Mech. Anal. (to appear).Google Scholar
  2. [2]
    H. ATTOUCH-C. SBORDONE, Asymptotic limits for perturbed functionals of Calculus of Variations, Ricerche di Mat., XXIX (1), 85–124 (1980).MathSciNetzbMATHGoogle Scholar
  3. [3]
    H.ATTOUCH-C.SBORDONE, A general homogenization formula for functionals of Calculus of Variations (to appear).Google Scholar
  4. [4]
    J.M. BALL, Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rational Mech. Anal. 63, 337–403 (1977).MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    L.D. BERKOWITZ, Lower semicontinuity of integral functionals, Trans. Am. Math. Soc. 192, 51–57 (1974).MathSciNetCrossRefGoogle Scholar
  6. [6]
    M. BONI, Su una definizione dell’integrale multiplo del Calcolo delle Variazioni, Atti Sem. Mat. Fis. Univ. Modena, XIX, (1), 86–106 (1970).MathSciNetzbMATHGoogle Scholar
  7. [7]
    G. BUTTAZZO-G. DAL MASO, Integral representation on w1,α (Ω) and BV(Ω) of limits of variational integrals, Rend. Acc. Naz. Lincei LXVI 5, 338–343 (1979).Google Scholar
  8. [8]
    L. CARBONE-C. SBORDONE, Some properties of Γ-limits of integral functionals, Annali Mat. Pura Appl. IV 122 1–60 (1979)MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    L. CESARI, Lower semicontinuity and lower closure theorems without seminormality condition, Annali Mat. Pura Appl. 98, 381–397 (1974).MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    B.DACOROGNA, A relaxation theorem and its application to the equilibrium of gases, Arch. Rational Mech. Anal. (to appear).Google Scholar
  11. [11]
    G. DAL MASO, Integral representation on BV(Ω) of Γ-limits of Variational Integrals, Manuscripta Math. 30, 387–416 (1980)MathSciNetCrossRefGoogle Scholar
  12. [12]
    G.DAL MASO-L.MODICA, A general theory of Variational Functionals (to appear)Google Scholar
  13. [13]
    E. DE GIORGI, Teoremi di semicontinuità nel Calcolo delle Variazioni, Ist.Naz. Alta Mat., Roma (1968–69)Google Scholar
  14. [14]
    E. DE GIORGI, Convergence problems for functionals and operators, Proc. Int. Meeting "Recent Methods in Nonlinear Analysis" Ed. E. De Giorgi-E. Magenes-U. Mosco, Pitagora, Bologna (1979).Google Scholar
  15. [15]
    I. EKELAND, Nonconvex minimization problems, Bull. Amer. Math. Soc. 1, (3), 443–474 (1979).MathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    I.EKELAND-R.TEMAM, Convex Analysis and Variational Problems, North Holland (1976).Google Scholar
  17. [17]
    F.FERRO, Integral characterization of functionals defined on spaces of BV functions, Rend. Sem. Mat. Univ. PadovaGoogle Scholar
  18. [18]
    N.FUSCO-G.MOSCARIELLO, L2-lower semicontinuity of functionals of quadratic type, Annali Mat. Pura Appl, (to appear).Google Scholar
  19. [19]
    F.W. GEHRING, The Lpintegrability of the partial derivatives of a quasiconformal mapping, Acta Mth. 130, 265–277 (1973).MathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    M.GIAQUINTA-E.GIUSTI, On the regularity of the minima of variational integrals, Acta Math.(to appear).Google Scholar
  21. [21]
    M. GIAQUINTA-G. MODICA, Regularity results for some classes of higher order non linear elliptic systems, J. fur Reine u. Angew. Math. 311/312, 145–169 (1979)MathSciNetzbMATHGoogle Scholar
  22. [22]
    M. GIAQUINTA,G. MODICA,J. SOUCEK, Functionals with linear growth in the Calculus of Variations, Comment. Math. Univ. Carolinae 20, 143–156 (1979)MathSciNetzbMATHGoogle Scholar
  23. [23]
    C. GOFFMAN-J. SERRIN, Sublinear functions of measures and variational integrals, Duke Math. J. 31, 159–178 (1964).MathSciNetCrossRefzbMATHGoogle Scholar
  24. [24]
    A. IOFFE,On Lower semicontinuity of integral functionals, SIAM J. Cont. Optimization 15, 521–538 (1977).MathSciNetCrossRefzbMATHGoogle Scholar
  25. [25]
    P. MARCELLINI, Some problems of semicontinuity and Γ-convergence for integrals of the Calculus of Variations, Proc. Int. Meeting "Recent Methods in Nonlinear Analysis" Ed. E. De Giorgi,E. Magenes,U. Mosco, Pitagora, Bologna (1979).Google Scholar
  26. [26]
    P. MARCELLINI-C. SBORDONE, Semicontinuity problems in the Calculus of Variations, Nonlinear Analysis TMA, 4 (2) 241–257 (1980)MathSciNetCrossRefzbMATHGoogle Scholar
  27. [27]
    P.MARCELLINI-C.SBORDONE, On the existence of minima of multiple integrals of the Calculus of Variations, J.Math.Pures Appl. (to appear).Google Scholar
  28. [28]
    C.B. MORREY, Quasiconvexity and the lower semicontinuity of multiple integrals,Pacific J. Math. 2 25–53 (1952).MathSciNetCrossRefzbMATHGoogle Scholar
  29. [29]
    C. OLECH, A characterization of L1-weak lower semicontinuity of integral functionals, Bull. Acad. Pol. Sci. Ser. Sci. Math. Astron. Phys. 25 135–142 (1977).MathSciNetzbMATHGoogle Scholar
  30. [30]
    L.A. PELETIER-J. SERRIN, Gradient bounds and Liouville theorems for quasilinear elliptic equations, Annali Sc. Norm. Sup. Pisa IV 5, 65–104 (1978).MathSciNetzbMATHGoogle Scholar
  31. [31]
    J.G. RESHETNYAK, Mapping with bounded deformation as extremals of Dirichlet type integrals, Siberian Math.J. 9, 487–498 (1968)CrossRefzbMATHGoogle Scholar
  32. [32]
    C.SBORDONE, Lower semicontinuity and regularity of minima of variational functionals, Nonlinear Partial Diff. Eq. and Their Applications, College de France Seminar, Vol. IV (to appear).Google Scholar
  33. [33]
    J. SERRIN, On the definition and properties of certain variational integrals, Trans. Amer. Math.Soc. 101 139–167 (1961).MathSciNetCrossRefzbMATHGoogle Scholar
  34. [34]
    J. SERRIN, Liouville Theorems and gradient bounds for quasilinear elliptic systems, Archive Rational Mech. Anal. 66, 295–310 (1977).MathSciNetCrossRefzbMATHGoogle Scholar
  35. [35]
    K.O. WIDMAN, Holder continuity of solutions of elliptic systems, Manuscripta Math. 5, 299–308 (1971).MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  1. 1.Istituto Matematico "R.Caccioppoli"Università di NapoliNapoliItaly

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