no. 1
Uniqueness of stable Meissner state solutions of the Chern-Simons-Higgs energy
ESAIM: Control, Optimisation and Calculus of Variations, Tome 16 (2010) no. 1, pp. 23-36.

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.

DOI : 10.1051/cocv:2008062
Classification : 35J50, 49J45
Mots clés : Chern-Simons-Higgs theory, superconductivity, uniqueness, meissner solution 
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     title = {Uniqueness of stable {Meissner} state solutions of the {Chern-Simons-Higgs} energy},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {23--36},
     publisher = {EDP-Sciences},
     volume = {16},
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     year = {2010},
     doi = {10.1051/cocv:2008062},
     mrnumber = {2598086},
     zbl = {1186.35054},
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Spirn, Daniel; Yan, Xiaodong. Uniqueness of stable Meissner state solutions of the Chern-Simons-Higgs energy. ESAIM: Control, Optimisation and Calculus of Variations, Tome 16 (2010) no. 1, pp. 23-36. doi : 10.1051/cocv:2008062. http://archive.numdam.org/articles/10.1051/cocv:2008062/

[1] L. Almeida and F. Bethuel, Topological methods for the Ginzburg-Landau equations. J. Math. Pures. Appl. 77 (1998) 1-49. | Zbl

[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. | Zbl

[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. | Zbl

[4] K. Choe and H.-S. Nam, Existence and uniqueness of topological multivortex solutions of the self-dual Chern-Simons CP(1) model. Nonlinear Anal. 66 (2007) 2794-2813. | Zbl

[5] M. Kurzke and D. Spirn, Gamma limit of the nonself-dual Chern-Simons-Higgs energy. J. Funct. Anal. 244 (2008) 535-588. | Zbl

[6] M. Kurzke and D. Spirn, Scaling limits of the Chern-Simons-Higgs energy. Commun. Contemp. Math. 10 (2008) 1-16.

[7] F. Pacard and T. Rivière, Linear and nonlinear aspects of vortices. The Ginzburg-Landau model. Progress in Nonlinear Differential Equations and their Applications 39. Birkhäuser Boston, Inc., Boston, MA, USA (2000). | Zbl

[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 Linéaire 17 (2000) 119-145. | Numdam | Zbl

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

[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). | MR | Zbl

[11] G. Tarantello, Uniqueness of selfdual periodic Chern-Simons vortices of topological-type. Calc. Var. Partial Differ. Equ. 29 (2007) 191-217. | MR | Zbl

[12] D. Ye and F. Zhou, Uniqueness of solutions of the Ginzburg-Landau problem. Nonlinear Anal. 26 (1996) 603-612. | MR | Zbl

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