© 2006

Topics on Concentration Phenomena and Problems with Multiple Scales

  • Andrea Braides
  • Valeria Chiadò Piat

Part of the Lecture Notes of the Unione Matematica Italiana book series (UMILN, volume 2)

Table of contents

  1. Front Matter
    Pages I-XI
  2. Problems with multiple scales

    1. Front Matter
      Pages 1-1
    2. Anneliese Defranceschi
      Pages 79-138
    3. Roberto Peirone
      Pages 139-188
    4. Gregory A. Chechkin
      Pages 189-208
  3. Problems with concentration

  4. Back Matter
    Pages 315-317

About this book


The study of variational problems showing multi-scale behaviour with oscillation or concentration phenomena are a challenging topic of very active research. This volume includes lecture notes devoted to the asymptotic analysis of such problems when the multi-scale behaviour derives from scale separation in the passage from atomistic systems to continuous functionals, from competition between bulk and surface energies, from various types of homogenization processes (random, in perforated domains, on fractals), and to concentration effects in Ginzburg-Landau energies and in subcritical growth problems.


Gamma-convergence Ginzburg-Landau equations concentration phenomena homogenization multiple-scale problems partial differential equation

Editors and affiliations

  • Andrea Braides
    • 1
  • Valeria Chiadò Piat
    • 2
  1. 1.Dipartimento di MatematicaUniversità di Roma “Tor Vergata”RomaItaly
  2. 2.Dipartimento di MatematicaPolitecnico di TorinoTorinoItaly

Bibliographic information