Geometric Partial Differential Equations

1. Front Matter

   Pages i-xiii

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2. On the structure of phase transition maps for three or more coexisting phases

   • Nicholas D. Alikakos

   Pages 1-31

3. The nonlinear multidomain model: a new formal asymptotic analysis

   • Stefano Amato, Giovanni Bellettini, Maurizio Paolini

   Pages 33-74

4. Existence and qualitative properties of isoperimetric sets in periodic media

   • Antonin Chambolle, Michael Goldman, Matteo Novaga

   Pages 75-92

5. Minimizing movements and level set approaches to nonlocal variational geometric flows

   • Antonin Chambolle, Massimiliano Morini, Marcello Ponsiglione

   Pages 93-104

6. Homogenization with oscillatory Neumann boundary data in general domain

   • Sunhi Choi, Inwon C. Kim

   Pages 105-118

7. The analysis of shock formation in 3-dimensional fluids

   • Demetrios Christodoulou

   Pages 119-138

8. Regularity of the extremal solutions for the Liouville system

   • Louis Dupaigne, Alberto Farina, Boyan Sirakov

   Pages 139-144

9. On general existence results for one-dimensional singular diffusion equations with spatially inhomogeneous driving force

   • Mi-Ho Giga, Yoshikazu Giga, Atsushi Nakayasu

   Pages 145-170

10. On representation of boundary integrals involving the mean curvature for mean-convex domains

    • Yoshikazu Giga, Giovanni Pisante

    Pages 171-187

11. Boundary regularity for the Poisson equation in reifenberg-flat domains

    • Antoine Lemenant, Yannick Sire

    Pages 189-209

12. Limiting models in condensed matter Physics and gradient flows of 1-homogeneous functional

    • Matteo Novaga, Giandomenico Orlandi

    Pages 211-226

13. Maximally localized Wannier functions: existence and exponential localization

    • Adriano Pisante

    Pages 227-250

14. Flows by powers of centro-affine curvature

    • Alina Stancu

    Pages 251-265

15. Back Matter

    Pages 267-268

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This book is the outcome of a conference held at the Centro De Giorgi of the Scuola Normale of Pisa in September 2012. The aim of the conference was to discuss recent results on nonlinear partial differential equations, and more specifically geometric evolutions and reaction-diffusion equations. Particular attention was paid to self-similar solutions, such as solitons and travelling waves, asymptotic behaviour, formation of singularities and qualitative properties of solutions. These problems arise in many models from Physics, Biology, Image Processing and Applied Mathematics in general, and have attracted a lot of attention in recent years.

• calculus of variations
• geometric analysis
• mathematical analysis
• partial differential equations

• CMAP, Ecole Polytechnique, CNRS, Palaiseau Cedex, France

  Antonin Chambolle

• Dipartimento di Matematica, Università di Pisa, Pisa, Italia

  Matteo Novaga

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