Variational Problems in Materials Science

  • Gianni dal Maso
  • Antonio DeSimone
  • Franco Tomarelli
Conference proceedings

Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 68)

Table of contents

  1. Front Matter
    Pages i-x
  2. Katayun Barmak, David Kinderlehrer, Irine Livshits, Shlomo Ta’asan
    Pages 1-11
  3. Andrea Braides, Valeria Chiadò Piat
    Pages 13-24
  4. Giuseppe Buttazzo, Marc Oliver Rieger
    Pages 25-41
  5. Gianpietro Del Piero
    Pages 43-54
  6. Giovanni De Matteis, Epifanio G. Virga
    Pages 55-74
  7. Gilles A. Francfort
    Pages 85-110
  8. Adriana Garroni, Giampiero Palatucci
    Pages 111-126
  9. Danilo Percivale, Franco Tomarelli
    Pages 127-136
  10. Paolo Podio-Guidugli
    Pages 137-147
  11. Augusto Visintin
    Pages 149-159
  12. Back Matter
    Pages 161-161

About these proceedings


This volume contains the proceedings of the international workshop Variational Problems in Materials Science, which was jointly organized by the International School for Advanced Studies (SISSA) of Trieste and by the Dipartimento di Matematica
``Francesco Brioschi'' of the Politecnico di Milano. The conference took place at SISSA from September 6 to 10, 2004.

The study of variational problems in materials science has a long history, and it has contributed a lot in shaping our understanding on how materials work and perform. There is, however, a recent renewed interest in this subject as a consequence of the fruitful interaction between mathematical analysis and the modelling of new, technologically advanced materials. On one hand, a sizable group of analysts has found in materials science a valuable source of inspiration for new variational theories and interesting problems. On the other hand, workers in the fields of theoretical, applied, and computational mechanics are increasingly using innovative variational techniques. The workshop intended to review some of the recent advances stemming from the successful interaction between the two communities, and to identify promising areas for further cooperation.

Talks were devoted to a wide spectrum of analytical techniques and of physical systems and phenomena. They included the study of BV vector fields, path functionals over Wasserstein spaces, variational approaches to quasi-static evolution, free-discontinuity problems with applications to fracture and plasticity, systems with hysteresis or with interfacial energies, evolution of interfaces, multi-scale analysis in ferromagnetism
and ferroelectricity, variational techniques for the study of crystal plasticity, of dislocations, and of concentrations in Ginzburg-Landau functionals, concentrated contact interactions, and phase transitions in biaxial liquid crystals. This volume collects contributions authored or co-authored by 11 of the 20 speakers invited to deliver lectures at the workshop. They all contain original results in fields which are at the forefront of current research, and in rapid evolution.



Boundary value problem computational mechanics electricity evolution equations materials science mechanics modeling plasticity variational problem

Editors and affiliations

  • Gianni dal Maso
    • 1
  • Antonio DeSimone
    • 1
  • Franco Tomarelli
    • 2
  1. 1.Scuola Internazionale Superiore di Studi Avanzati (SISSA)TriesteItaly
  2. 2.Dipartimento di Matematica “Francesco Brioschi”Politecnico di MilanoMilanoItaly

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