Uniqueness of stable Meissner state solutions of the Chern-Simons-Higgs energy

Daniel Spirn; Xiaodong Yan

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 16, Issue: 1, page 23-36
  • ISSN: 1292-8119

Abstract

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For external magnetic field hex ≤ Cε–α, we prove that a Meissner state solution for the Chern-Simons-Higgs functional exists. Furthermore, if the solution is stable among all vortexless solutions, then it is unique.

How to cite

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Spirn, Daniel, and Yan, Xiaodong. "Uniqueness of stable Meissner state solutions of the Chern-Simons-Higgs energy." ESAIM: Control, Optimisation and Calculus of Variations 16.1 (2010): 23-36. <http://eudml.org/doc/250745>.

@article{Spirn2010,
abstract = { For external magnetic field hex ≤ Cε–α, we prove that a Meissner state solution for the Chern-Simons-Higgs functional exists. Furthermore, if the solution is stable among all vortexless solutions, then it is unique.},
author = {Spirn, Daniel, Yan, Xiaodong},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Chern-Simons-Higgs theory; superconductivity; uniqueness; Meissner solution},
language = {eng},
month = {1},
number = {1},
pages = {23-36},
publisher = {EDP Sciences},
title = {Uniqueness of stable Meissner state solutions of the Chern-Simons-Higgs energy},
url = {http://eudml.org/doc/250745},
volume = {16},
year = {2010},
}

TY - JOUR
AU - Spirn, Daniel
AU - Yan, Xiaodong
TI - Uniqueness of stable Meissner state solutions of the Chern-Simons-Higgs energy
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/1//
PB - EDP Sciences
VL - 16
IS - 1
SP - 23
EP - 36
AB - For external magnetic field hex ≤ Cε–α, we prove that a Meissner state solution for the Chern-Simons-Higgs functional exists. Furthermore, if the solution is stable among all vortexless solutions, then it is unique.
LA - eng
KW - Chern-Simons-Higgs theory; superconductivity; uniqueness; Meissner solution
UR - http://eudml.org/doc/250745
ER -

References

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  2. F. Bethuel, H. Brezis and F. Hélein, Asymptotics for the minimization of a Ginzburg-Landau functional. Cal. Var. Partial Differ. Equ.1 (1993) 123–148.  Zbl0834.35014
  3. A. Bonnet, S.J. Chapman and R. Monneau, Convergence of Meissner minimizers of the Ginzburg-Landau energy of superconductivity as κ → +∞. SIAM J. Math. Anal.31 (2000) 1374–1395.  Zbl0970.35031
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  7. F. Pacard and T. Rivière, Linear and nonlinear aspects of vortices. The Ginzburg-Landau model. Progress in Nonlinear Differential Equations and their Applications39. Birkhäuser Boston, Inc., Boston, MA, USA (2000).  Zbl0948.35003
  8. E. Sandier and S. Serfaty, Global minimizers for the Ginzburg-Landau functional below the first critical magnetic field. Ann. Inst. H. Poincaré, Anal. Non Linéaire17 (2000) 119–145.  Zbl0947.49004
  9. S. Serfaty, Stable configurations in superconductivity: Uniqueness, mulitplicity, and vortex-nucleation. Arch. Rational Mech. Anal.149 (1999) 329–365.  Zbl0959.35154
  10. D. Spirn and X. Yan, Minimizers near the first critical field for the nonself-dual Chern-Simons-Higgs energy. Calc. Var. Partial Differ. Equ. (to appear).  Zbl1169.35019
  11. G. Tarantello, Uniqueness of selfdual periodic Chern-Simons vortices of topological-type. Calc. Var. Partial Differ. Equ.29 (2007) 191–217.  Zbl1123.35050
  12. D. Ye and F. Zhou, Uniqueness of solutions of the Ginzburg-Landau problem. Nonlinear Anal.26 (1996) 603–612.  Zbl0855.49002

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