Local Minimization, Variational Evolution and Γ-Convergence

  • Andrea Braides

Part of the Lecture Notes in Mathematics book series (LNM, volume 2094)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Andrea Braides
    Pages 1-6
  3. Andrea Braides
    Pages 7-24
  4. Andrea Braides
    Pages 53-66
  5. Andrea Braides
    Pages 67-78
  6. Andrea Braides
    Pages 79-89
  7. Andrea Braides
    Pages 91-101
  8. Andrea Braides
    Pages 129-143
  9. Andrea Braides
    Pages 145-158
  10. Andrea Braides
    Pages 159-171
  11. Back Matter
    Pages 173-176

About this book

Introduction

This book addresses new questions related to the asymptotic description of converging energies from the standpoint of local minimization and variational evolution. It explores the links between Gamma-limits, quasistatic evolution, gradient flows and stable points, raising new questions and proposing new techniques. These include the definition of effective energies that maintain the pattern of local minima, the introduction of notions of convergence of energies compatible with stable points, the computation of homogenized motions at critical time-scales through the definition of minimizing movement along a sequence of energies, the use of scaled energies to study long-term behavior or backward motion for variational evolutions. The notions explored in the book are linked to existing findings for gradient flows, energetic solutions and local minimizers, for which some generalizations are also proposed.

Keywords

49J45,74Q10,49J40,74Q05 Gamma-convergence Gradient flow Homogenization Local minimization Variational Evolution

Authors and affiliations

  • Andrea Braides
    • 1
  1. 1.Dipartimento di MatematicaUniversità di Roma Tor VergataRomaItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-01982-6
  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-01981-9
  • Online ISBN 978-3-319-01982-6
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book