Applied Mathematics and Optimization

, Volume 27, Issue 2, pp 105–123

Asymptotic development by Γ-convergence

  • Gabriele Anzellotti
  • Sisto Baldo


A description of the asymptotic development of a family of minimum problems is proposed by a suitable iteration of Γ-limit procedures. An example of asymptotic development for a family of functionals related to phase transformations is also given.

Key words

Γ-convergence Asymptotic developments BV functions 

AMS classification

Primary 49J45 Secondary 41A60 


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  1. [A]
    L. Ambrosio: Metric space valued functions of bounded variation. Preprint, Scuola Normale Superiore, Pisa, 1989.Google Scholar
  2. [AMT]
    L. Ambrosio, S. Mortola, V. Tortorelli: Functionals with linear growth defined on vector valued BV functions. J. Math. Pures Appl., to appear.Google Scholar
  3. [ABV]
    G. Anzellotti, S. Baldo, A. Visintin: Asymptotic behaviour of the Landau-Lifshitz model of ferromagnetism. Appl. Math. Optim., 23 (1991), 171–192.Google Scholar
  4. [B]
    S. Baldo: Minimal interface criterion for phase transitions in mixture of a Cahn-Hiliiard fluids. Ann. Inst. H. Poincaré Anal. Non Linéaire, to appear.Google Scholar
  5. [BB]
    S. Baldo, G. Bellettini: Γ-convergence and numerical analysis: an application to the minimal partition problem. Ricerche Mat., to appear.Google Scholar
  6. [BP]
    G. Buttazzo, D. Percivale: Preprint.Google Scholar
  7. [DM]
    G. Dal Maso, L. Modica: A general theory of variational integrals. “Topics in Functional Analysis 1980–81” Quaderno, Scuola Normale Superiore, Pisa, 1982, pp. 149–221.Google Scholar
  8. [DF]
    E. De Giorgi, T. Franzoni: Su un tipo di convergenza variazionale. Rend. Sem. Mat. Brescia, 3 (1979), 63–101.Google Scholar
  9. [F]
    H. Federer: Geometric Measure Theory. Springer-Verlag, Berlin, 1968.Google Scholar
  10. [FT]
    I. Fonseca, L. Tartar: The gradient theory of phase transitions for system with two potential wells, Proc. Roy. Soc. Edinburgh, 111A (1989), 89–102.Google Scholar
  11. [G]
    E. Giusti: Minimal surfaces and functions of bounded variation. Birkhäuser, Boston, 1984.Google Scholar
  12. [Ml]
    L. Modica: Gradient theory for phase transitions and the minimal interface criterion. Arch. Rat. Mech. Anal., 98 (1987), 123–142.Google Scholar
  13. [M2]
    L. Modica: Gradient theory of phase transitions with boundary contact energy. Ann. Inst. H. Poincaré Anal. Non Linéaire, 4 (1987), 487–512.Google Scholar
  14. [MM]
    L. Modica, S. Mortola: Un esempio di Γ-convergenza, Boll. Un. Mat. Ital. B (5), 14 (1977), 285–299.Google Scholar
  15. [OS]
    N. Owen, P. Sternberg: Nonconvex variational problems with anisotropic perturbations, to appear.Google Scholar
  16. [S]
    P. Sternberg: The effect of a singular perturbation on nonconvex variational problems. Ph.D. Thesis, New York University, 1986.Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1993

Authors and Affiliations

  • Gabriele Anzellotti
    • 1
  • Sisto Baldo
    • 1
  1. 1.Dipartimento di MatematicaUniversità Degli Studi di TrentoPovo, (Trento)Italy

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