Different Time Scales

  • Andrea Braides
Part of the Lecture Notes in Mathematics book series (LNM, volume 2094)


In this section we examine the effect of scaling the energies in the resulting minimizing movements. One application is the possibility of defining and study long-time behaviour of variational motions, such as the ones connected to Mumford–Shah or Perona–Malik energies, Lennard-Jones discrete systems, or the gradient theory of phase transitions. These are obtained by suitably choosing a diverging (but positive) scaling of the energies. Negative scalings may be used to define a backward motion of some energy F, after properly choosing a family of functional Γ-converging to F.


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    Bronsard, L., Kohn, R.V.: On the slowness of phase boundary motion in one space dimension. Comm. Pure Appl. Math. 43, 983–997 (1990)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Braides, A., Scilla, G.: Nucleation and backward motion of discrete interfaces. Preprint Scuola Normale Superiore, Pisa (2013).

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Andrea Braides
    • 1
  1. 1.Dipartimento di MatematicaUniversità di Roma Tor VergataRomaItaly

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