On the Third Critical Field \(H_{C_3}\)

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


Using the spectral asymptotics of the Neumann Laplacian with magnetic field, we give precise estimates on the critical field \(H_{C_3}\), describing the onset of superconductivity in type II superconductors. Furthermore, we prove that the definitions of this field corresponding to local minimizers and global minimizers coincide.


Nontrivial Solution Ground State Energy Critical Field Sobolev Inequality Connected Domain 
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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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