Between \(H_{C_2}\) and \(H_{C_3}\) in Two Dimensions

  • Søren Fournais
  • Bernard Helffer
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 77)


Between \(H_{C_2}\)(k) and \(H_{C_3}\)(k), superconductivity is for large k confined to the boundary. This follows from the decay estimates in Chapter 12. In the present chapter, we will give leading-order energy estimates in this parameter region, which are valid when we are not too close to either of the critical fields. These energy estimates indicate that superconductivity is essentially uniformly distributed over the entire boundary region.


Ground State Energy Implicit Function Theorem Decay Estimate Present Chapter Dimension Proof 
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Copyright information

© Birkhäuser Boston 2009

Authors and Affiliations

  1. 1.Department of Mathematical SciencesAarhus UniversityAarhus CDenmark
  2. 2.Département de MathématiquesUniversité Paris-Sud and CNRSOrsay CedexFrance

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