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Geometric Partial Differential Equations

  • Conference proceedings
  • © 2013

Overview

Editors:
  1. Antonin Chambolle

    1. CMAP, Ecole Polytechnique, CNRS, Palaiseau Cedex, France

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  2. Matteo Novaga

    1. Dipartimento di Matematica, Università di Pisa, Pisa, Italia

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  3. Enrico Valdinoci
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  • Presentation of selected topics of current research in geometric partial differential equations
  • Authors are recognized international experts

Part of the book series: Publications of the Scuola Normale Superiore (PSNS, volume 15)

Part of the book sub series: CRM Series (CRMSNS)

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Table of contents (13 papers)

  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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Keywords

About this book

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.

Editors and Affiliations

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

    Antonin Chambolle

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

    Matteo Novaga

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