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On the Ginzburg-Landau critical field in three dimensions

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  • Department of Mathematical Sciences
  • Teoretisk naturvidenskab
We study the three-dimensional Ginzburg-Landau model of superconductivity. Several natural definitions of the (third) critical field, HC3, governing the transition from the superconducting state to the normal state, are considered. We analyze the relation between these fields and give conditions as to when they coincide. An interesting part of the analysis is the study of the monotonicity of the ground state energy of the Laplacian with constant magnetic field and with Neumann (magnetic) boundary condition in a domain . It is proved that the ground state energy is a strictly increasing function of the field strength for sufficiently large fields. As a consequence of our analysis, we give an affirmative answer to a conjecture by Pan. © 2008 Wiley Periodicals, Inc.
Original languageEnglish
JournalCommunications on Pure and Applied Mathematics
Pages (from-to)215-241
Number of pages27
Publication statusPublished - 2009

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