Vortex pinning with bounded fields for the Ginzburg–Landau equation

Nelly Andre; Patricia Bauman; Dan Phillips

Annales de l'I.H.P. Analyse non linéaire (2003)

  • Volume: 20, Issue: 4, page 705-729
  • ISSN: 0294-1449

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Andre, Nelly, Bauman, Patricia, and Phillips, Dan. "Vortex pinning with bounded fields for the Ginzburg–Landau equation." Annales de l'I.H.P. Analyse non linéaire 20.4 (2003): 705-729. <http://eudml.org/doc/78594>.

@article{Andre2003,
author = {Andre, Nelly, Bauman, Patricia, Phillips, Dan},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Ginzburg-Landau free energy; non-uniform superconductivity; minimizers; vortex patterns},
language = {eng},
number = {4},
pages = {705-729},
publisher = {Elsevier},
title = {Vortex pinning with bounded fields for the Ginzburg–Landau equation},
url = {http://eudml.org/doc/78594},
volume = {20},
year = {2003},
}

TY - JOUR
AU - Andre, Nelly
AU - Bauman, Patricia
AU - Phillips, Dan
TI - Vortex pinning with bounded fields for the Ginzburg–Landau equation
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2003
PB - Elsevier
VL - 20
IS - 4
SP - 705
EP - 729
LA - eng
KW - Ginzburg-Landau free energy; non-uniform superconductivity; minimizers; vortex patterns
UR - http://eudml.org/doc/78594
ER -

References

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  2. [2] Bethuel F., The approximation problem for Sobolev maps between two manifolds, Acta Math.167 (3–4) (1991) 153-206. Zbl0756.46017MR1120602
  3. [3] Chapman S.J., Du Q., Gunzburger M.D., A Ginzburg–Landau type model of superconducting/normal junctions including Josephson junctions, Europ. J. Appl. Math.6 (1995) 97-114. Zbl0843.35120MR1331493
  4. [4] Chapman S.J., Richardson G., Vortex pinning by inhomogeneities in type II superconductors, Phys. D108 (4) (1997) 397-407. Zbl1039.82510MR1474691
  5. [5] Giorgi T., Phillips D., The breakdown of superconductivity due to strong fields for the Ginzburg–Landau model, SIAM J. Math. Anal.30 (2) (1999) 341-359. Zbl0920.35058MR1664763
  6. [6] Jaffe A., Taubes C., Vortices Monopoles, Birkhäuser, 1980. Zbl0457.53034MR614447
  7. [7] Jerrard R., Lower bounds for generalized Ginzburg–Landau functionals, SIAM J. Math. Anal.30 (4) (1999) 721-746. Zbl0928.35045MR1684723
  8. [8] Jimbo S., Morita Y., Ginzburg–Landau equations and stable solutions in a rotational domain, SIAM J. Math. Anal.27 (5) (1996) 1360-1385. Zbl0865.35016MR1402445
  9. [9] Jimbo S., Zhai J., Ginzburg–Landau equation with magnetic effect: non-simply-connected domains, J. Math. Soc. Japan50 (3) (1998) 663-684. Zbl0912.58011MR1626354
  10. [10] Likharev K., Superconducting weak links, Rev. Mod. Phys.51 (1979) 101-159. 
  11. [11] E. Sandier, S. Serfaty, Global minimizers for the Ginzburg–Landau functional below the first critical magnetic field, Annals IHP, Analyse non linéaire, to appear. Zbl0947.49004MR1743433
  12. [12] E. Sandier, S. Serfaty, On the energy of type II superconductors in the mixed phase, Rev. Math. Phys., to appear. Zbl0964.49006MR1794239
  13. [13] Rubinstein J., Sternberg P., Homotopy classification of minimizers of the Ginzburg–Landau energy and the existence of permanent currents, Comm. Math. Phys.179 (1) (1996) 257-263. Zbl0860.35131MR1395224
  14. [14] Schoen R., Uhlenbeck K., Boundary regularity and the Dirichlet problem for harmonic maps, J. Differential Geom.18 (2) (1983) 253-268. Zbl0547.58020MR710054

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