Variational Methods for Discontinuous Structures

1. Front Matter

   Pages I-VIII

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2. Movimenti di Partizioni

   • Ennio De Giorgi

   Pages 1-5

3. The Crystalline Algorithm for Computing Motion by Curvature

   • Pedro Martins Girão, Robert V. Kohn

   Pages 7-18

4. Uses of Elliptic Approximations in Computer Vision

   • Jayant Shah

   Pages 19-34

5. A Kanizsa Programme

   • Vicent Caselles, Bartomeu Coll, Jean-Michel Morel

   Pages 35-55

6. A Second Order Model in Image Segmentation: Blake & Zisserman Functional

   • Michele Carriero, Antonio Leaci, Franco Tomarelli

   Pages 57-72

7. Optimal Approximation by Piecewise Constant Functions

   • Italo Tamanini

   Pages 73-85

8. Indefinite Superlinear Elliptic Problems

   • Italo Capuzzo Dolcetta

   Pages 87-92

9. On the Regularity of the Edge Set of Mumford-Shah Minimizers

   • Alexis Bonnet

   Pages 93-103

10. Capacity and Dirichlet Problems in varying Domains

    • Gianni Dal Maso

    Pages 105-110

11. General Growth Conditions and Regularity

    • Paolo Marcellini

    Pages 111-118

12. Geodesic Lines in Metric Spaces

    • Mario Miranda

    Pages 119-122

13. Flow by Mean Curvature of Surfaces of Any Codimension

    • Luigi Ambrosio, Halil Mete Soner

    Pages 123-134

14. Functions of Bounded Variation over Non-Smooth Manifolds and Generalized Curvatures

    • Gabriele Anzellotti

    Pages 135-142

15. Remarks on a Numerical Study of Convexity, Quasiconvexity, and Rank One Convexity

    • Bernard Dacorogna, Jean-Pierre Haeberly

    Pages 143-154

16. Homogeneous Fractal Spaces

    • Umberto Mosco, Lino Notarantonio

    Pages 155-160

17. Variational Techniques for Problems in Materials Science

    • Irene Fonseca

    Pages 161-175

18. Magnetoelastic Interactions

    • David Kinderlehrer

    Pages 177-189

19. Back Matter

    Pages 191-196

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In recent years many researchers in material science have focused their attention on the study of composite materials, equilibrium of crystals and crack distribution in continua subject to loads. At the same time several new issues in computer vision and image processing have been studied in depth. The understanding of many of these problems has made significant progress thanks to new methods developed in calculus of variations, geometric measure theory and partial differential equations. In particular, new technical tools have been introduced and successfully applied. For example, in order to describe the geometrical complexity of unknown patterns, a new class of problems in calculus of variations has been introduced together with a suitable functional setting: the free-discontinuity problems and the special BV and BH functions. The conference held at Villa Olmo on Lake Como in September 1994 spawned successful discussion of these topics among mathematicians, experts in computer science and material scientists.

• Calculus of Variations
• Finite
• Manifold
• calculus
• equation
• function
• partial differential equation

• Dipartimento di Matematica, Politecnico di Milano, Milano, Italy

  Raul Serapioni, Franco Tomarelli

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