Spectral Methods in Surface Superconductivity

  • Søren Fournais
  • Bernard Helffer

Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 77)

Table of contents

  1. Front Matter
    Pages I-XX
  2. Linear Analysis

    1. Front Matter
      Pages 1-1
    2. Søren Fournais, Bernard Helffer
      Pages 3-17
    3. Søren Fournais, Bernard Helffer
      Pages 19-30
    4. Søren Fournais, Bernard Helffer
      Pages 31-43
    5. Søren Fournais, Bernard Helffer
      Pages 45-50
    6. Søren Fournais, Bernard Helffer
      Pages 51-65
    7. Søren Fournais, Bernard Helffer
      Pages 67-77
    8. Søren Fournais, Bernard Helffer
      Pages 117-137
  3. Nonlinear Analysis

    1. Front Matter
      Pages 140-140
    2. Søren Fournais, Bernard Helffer
      Pages 141-156
    3. Søren Fournais, Bernard Helffer
      Pages 157-178
    4. Søren Fournais, Bernard Helffer
      Pages 179-192
    5. Søren Fournais, Bernard Helffer
      Pages 193-207
    6. Søren Fournais, Bernard Helffer
      Pages 209-238
    7. Søren Fournais, Bernard Helffer
      Pages 239-260
    8. Søren Fournais, Bernard Helffer
      Pages 261-268
  4. Back Matter
    Pages 269-324

About this book

Introduction

During the past decade, the mathematics of superconductivity has been the subject of intense activity. This book examines in detail the nonlinear Ginzburg–Landau functional, the model most commonly used in the study of superconductivity. Specifically covered are cases in the presence of a strong magnetic field and with a sufficiently large Ginzburg–Landau parameter kappa.

Key topics and features of the work:

* Provides a concrete introduction to techniques in spectral theory and partial differential equations
* Offers a complete analysis of the two-dimensional Ginzburg–Landau functional with large kappa in the presence of a magnetic field
* Treats the three-dimensional case thoroughly
* Includes open problems

Spectral Methods in Surface Superconductivity is intended for students and researchers with a graduate-level understanding of functional analysis, spectral theory, and the analysis of partial differential equations. The book also includes an overview of all nonstandard material as well as important semi-classical techniques in spectral theory that are involved in the nonlinear study of superconductivity.

Keywords

Ginzburg–Landau functional Potential functional analysis magnetic fields optimal elliptic estimates parameter kappa spectral theory superconductivity

Authors and affiliations

  • Søren Fournais
    • 1
  • Bernard Helffer
    • 2
  1. 1.Department of Mathematical SciencesUniversity of AarhusAarhus CDenmark
  2. 2., Département de MathématiquesUniversité Paris-Sud and CNRSOrsay CedexFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-8176-4797-1
  • Copyright Information Springer Science+Business Media, LLC 2010
  • Publisher Name Birkhäuser Boston
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-8176-4796-4
  • Online ISBN 978-0-8176-4797-1
  • About this book