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The ground state energy of the three dimensional Ginzburg-Landau functional. Part II: Surface regime

Fournais, Søren ; Kachmar, Ayman and Persson Sundqvist, Mikael LU (2013) In Journal des Mathématiques Pures et Appliquées 99(3). p.343-374
Abstract
We study the Ginzburg-Landau model of superconductivity in three dimensions and for strong external magnetic fields. For magnetic field strengths above the phenomenologically defined second critical field it is known from Physics that superconductivity should be essentially restricted to a region near the boundary. We prove that the expected region does indeed carry superconductivity. Furthermore, we give precise energy estimates valid also in the regime around the second critical field which display the transition from bulk superconductivity to surface superconductivity. (C) 2012 Elsevier Masson SAS. All rights reserved.
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author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Ginzburg-Landau functional, Thermodynamic limits, Elliptic estimates, Variational methods, Magnetic Schrodinger operators, Semiclassical, analysis
in
Journal des Mathématiques Pures et Appliquées
volume
99
issue
3
pages
343 - 374
publisher
Elsevier
external identifiers
  • wos:000326359700007
  • scopus:84873570698
ISSN
0021-7824
DOI
10.1016/j.matpur.2012.09.002
language
English
LU publication?
yes
id
16afa2d8-c7c1-4a6c-a2fb-9d6b3e4d0ab4 (old id 4215933)
date added to LUP
2016-04-01 13:50:48
date last changed
2022-04-14 03:27:23
@article{16afa2d8-c7c1-4a6c-a2fb-9d6b3e4d0ab4,
  abstract     = {{We study the Ginzburg-Landau model of superconductivity in three dimensions and for strong external magnetic fields. For magnetic field strengths above the phenomenologically defined second critical field it is known from Physics that superconductivity should be essentially restricted to a region near the boundary. We prove that the expected region does indeed carry superconductivity. Furthermore, we give precise energy estimates valid also in the regime around the second critical field which display the transition from bulk superconductivity to surface superconductivity. (C) 2012 Elsevier Masson SAS. All rights reserved.}},
  author       = {{Fournais, Søren and Kachmar, Ayman and Persson Sundqvist, Mikael}},
  issn         = {{0021-7824}},
  keywords     = {{Ginzburg-Landau functional; Thermodynamic limits; Elliptic estimates; Variational methods; Magnetic Schrodinger operators; Semiclassical; analysis}},
  language     = {{eng}},
  number       = {{3}},
  pages        = {{343--374}},
  publisher    = {{Elsevier}},
  series       = {{Journal des Mathématiques Pures et Appliquées}},
  title        = {{The ground state energy of the three dimensional Ginzburg-Landau functional. Part II: Surface regime}},
  url          = {{http://dx.doi.org/10.1016/j.matpur.2012.09.002}},
  doi          = {{10.1016/j.matpur.2012.09.002}},
  volume       = {{99}},
  year         = {{2013}},
}