| Abstract: |
| Let $(u_\varepsilon)$ be a family of solutions of the Ginzburg--Landau equation
with boundary condition $u_\varepsilon = g$ on $\partial \Omega$ and of degree zero.
According to [Bethuel-Brezis-H\`{e}lein, 1993], the $H^1$ convergence of $u_\varepsilon$ is a key ingredient of uniform convergence.
In this talk, we give an equivalent condition for $H^1$ convergence.
Furthermore, we generalize it to multi-component Ginzburg-Landau equations.
We also talk about the recent progress of asymptotics of minimizers for the multi-component Ginzburg-Landau energy. |
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