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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  9. S. Serfaty, Stable configurations in superconductivity: Uniqueness, mulitplicity, and vortex-nucleation. Arch. Rational Mech. Anal.149 (1999) 329–365.  
  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).  
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