On the asymptotic behavior of minimizers of the Ginzburg-Landau model in $2$ dimensions
Michaël Struwe · Differential and Integral Equations · 1994
Minimizers uE of the Ginzburg-Landau energy EE defined in (1) below on an arbitrary domain n cc R 2 with smooth boundary and boundary data g: an ---+-S 1 as E ---+-0 are shown to subconverge weakly in H 1 •P for p < 2 and locally in H 1 • 2 away from finitely many points x1, ... , x1 to a smooth harmonic map u: n \ {xi, ... , x;} ---+-S 1 .The proof is based on simple comparison arguments.The result simplifies and extends previous work ofBethuel-Brezis-Helein for the same problem on a star-shaped domain.