Variational Methods for Discontinuous Structures

1. Front Matter

   Pages i-x

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2. A Model for Mixtures of Micromagnetic Materials allowing Existence and Regularity

   • Emilio Acerbi

   Pages 1-8

3. Variational Properties of a Model for Image Segmentation with Overlapping Regions

   • Giovanni Bellettini, Riccardo March

   Pages 9-17

4. Variational Theory of Weak Geometric Structures: The Measure Method and Its Applications

   • Guy Bouchitté, Ilaria Fragalà

   Pages 19-40

5. Optimal Transportation Problems with Free Dirichlet Regions

   • Giusppe Buttazzo, Edouard Oudet, Eugene Stepanov

   Pages 41-65

6. Local Minimizers for a Free Gradient Discontinuity Problem in Image Segmentation

   • Michele Carriero, Antonio Leaci, Franco Tomarelli

   Pages 67-80

7. Irrigation

   • Vicent Caselles, Jean-Michel Morel

   Pages 81-90

8. Symmetrization and Functionals Defined on BV

   • Andrea Cianchi, Nicola Fusco

   Pages 91-102

9. Interface Energies and Structured Deformations in Plasticity

   • Gianpietro Del Piero

   Pages 103-116

10. Higher Order Variational Problems and Phase Transitions in Nonlinear Elasticity

    • Irene Fonseca, Giovanni Leoni

    Pages 117-140

11. Unstable Crystalline Wulff Shapes in 3D

    • Maurizio Paolini, Franco Pasquarelli

    Pages 141-153

12. Dimension Reduction in Continuum Mechanics

    • Danilo Percivale

    Pages 155-170

13. Reaction-Diffusion Equations and Learning

    • Jayant Shah

    Pages 171-182

14. Back Matter

    Pages 183-188

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This volume contains the Proceedings of the International Workshop Variational Methods For Discontinuous Structures, which was jointly organized by the Dipar­ timento di Matematica Francesco Brioschi of Milano Politecnico and the Interna­ tional School for Advanced Studies (SISSA) of Trieste. The Conference took place at Villa Erba Antica (Cernobbio) on the Lago di Como on July 4- 6, 2001. In past years the calculus of variations faced mainly the study of continuous structures, say particularly problems with smooth solutions. One of the deepest and more delicate problems was the regularity of weak solutions. More recently, new sophisticated tools have been introduced in order to study discontinuities: in many variational problems solutions develop singularities, and sometimes the most interesting part of a solution is the singularity itself. The conference intended to focus on recent developments in this direction. Some of the talks were devoted to differential or variational modelling of image segmentation, occlusion and textures synthesizing in image analysis, varia­ tional description of micro-magnetic materials, dimension reduction and structured deformations in elasticity and plasticity, phase transitions, irrigation and drainage, evolution of crystalline shapes; in most cases theoretical and numerical analysis of these models were provided. viii Preface Other talks were dedicated to specific problems of the calculus of variations: variational theory of weak or lower-dimensional structures, optimal transport prob­ lems with free Dirichlet regions, higher order variational problems, symmetrization in the BV framework.

• Calculus of Variations
• Partial differential equations
• functional analysis
• numerical analysis
• partial differential equation

• Scuola Internazionale Superiore di Studi, Avanzati (SISSA), Trieste, Italy

  Gianni Maso

• Dipartimento di Matematica “Francesco Brioschi”, Politecnico di Milano, Milano, Italy

  Franco Tomarelli

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