TY - JOUR
T1 - On uniqueness of vector-valued minimizers of the ginzburg-landau functional in annular domains
AU - Golovaty, Dmitry
AU - Berlyand, Leonid
PY - 2002/3
Y1 - 2002/3
N2 - Consider a class of Sobolev functions satisfying a prescribed degree condition on the boundary of a planar annular domain. It is shown that, within this class, the Ginzburg-Landau functional possesses the unique, radially symmetric minimizer, provided that the annulus is sufficiently narrow. This result is known to be false for wide annuli where vortices are energetically feasible. The estimate for the critical radius below which the uniqueness of the minimizer is guaranteed is obtained as well.
AB - Consider a class of Sobolev functions satisfying a prescribed degree condition on the boundary of a planar annular domain. It is shown that, within this class, the Ginzburg-Landau functional possesses the unique, radially symmetric minimizer, provided that the annulus is sufficiently narrow. This result is known to be false for wide annuli where vortices are energetically feasible. The estimate for the critical radius below which the uniqueness of the minimizer is guaranteed is obtained as well.
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U2 - 10.1007/s005260100102
DO - 10.1007/s005260100102
M3 - Article
AN - SCOPUS:0036524673
SN - 0944-2669
VL - 14
SP - 213
EP - 232
JO - Calculus of Variations and Partial Differential Equations
JF - Calculus of Variations and Partial Differential Equations
IS - 2
ER -