Annali dell’Università’ di Ferrara

, Volume 34, Issue 1, pp 219–236 | Cite as

Necessary and sufficient conditions for the lower semicontinuity of certain integral functionals

  • Andrea Gavioli


Singular Point Lower Semicontinuity Weak Topology Lebesgue Point Equivalent Inte 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    L. Ambrosio,New semicontinuity results for integral functionals, to appear on Rendiconti dell'Accademia Nazionale delle Scienze detta dei XL.Google Scholar
  2. [2]
    C. Benassi—A. Gavioli,Some results about relaxation of integral functionals, to appear on Atti Sem. Mat. Fis. Univ. Modena.Google Scholar
  3. [3]
    G. Buttazzo—G. Dal Maso,Γ-limits of integral functionals, J. Analyse Math.,37 (1980).Google Scholar
  4. [4]
    G. ButtazzoG. Dal Maso,Integral representation and relaxation of local functionals, Nonlinear Anal.,9, no. 6 (1985), pp. 512–532.CrossRefGoogle Scholar
  5. [5]
    L. CarboneC. Sbordone,Some properties of Γ-limits of integral functionals, Annali di Matem. Pura e Appl., (4),122 (1979), pp. 1–60.MATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    G. Dal Maso,Integral representation of BV(Ω) of Γ-limits of variational integrals, Manuscripta Mathematica,30 (1980), pp. 387–416.MATHCrossRefGoogle Scholar
  7. [7]
    E. De GiorgiG. ButtazzoG. Dal Maso,On the lower semicontinuity of certain integral functionals, Atti Acc. Naz. Lincei, Rend. Cl. Sci. Fis. Mat. Natur., (8),74, no. 5 (1983), pp. 274–282.MATHGoogle Scholar
  8. [8]
    F. Ferro,Lower semicontinuity, optimization and regularizing extensions of integral functionals, S.I.A.M. J. Control Optim.,19, no. 4 (1981), pp. 433–444.MATHCrossRefMathSciNetGoogle Scholar
  9. [9]
    F. Ferro,Lower semicontinuity of integral functionals and applications. Boll. Un. Mat. Ital., (6),1-B (1982), pp. 753–762.MathSciNetGoogle Scholar
  10. [10]
    N. FuscoG. Moscariello,L 2 -lower semicontinuity of functionals of quadratic type, Annali di Matem. Pura e Appl., (4),129 (1981), pp. 305–326.MATHCrossRefMathSciNetGoogle Scholar
  11. [11]
    A. Gavioli,On the upper semicontinuity of the Hamiltonian, Atti Sem. Mat. Fis. Univ. Modena,30 (1981), pp. 138–150.MATHMathSciNetGoogle Scholar
  12. [12]
    A. Gavioli,A lower semicontinuity theorem for the integral of the Calculus of Variations, Atti Sem. Mat. Fis. Univ. Modena,31 (1982).Google Scholar
  13. [13]
    A. Grothendieck,Espaces vectoriels topologiques, S. Paulo, Brazil (1958).Google Scholar
  14. [14]
    R. T. Rockafellar,Convex analysis, Princeton University Press, Princeton, New Jersey (1970).MATHGoogle Scholar
  15. [15]
    R. T. Rockafellar,Integrals which are convex functionals, Pacific J. Math.,24 (1968), pp. 597–611.Google Scholar
  16. [16]
    R. T. Rockafellar,Integral functionals, normal integrands and measurable selections, Lecture Notes in Mathematics,543 (1976).Google Scholar
  17. [17]
    J. Serrin,On the definition and properties of certain variational integrals, Trans. Amer. Math. Soc.,101 (1961), pp. 139–167.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Università degli Studi di Ferrara 1988

Authors and Affiliations

  • Andrea Gavioli
    • 1
  1. 1.Dipartimento di Matematica Pura ed Applicata «G. Vitali»Università di ModenaModenaItalia

Personalised recommendations