Minimax Critical Points in Ginzburg-Landau Problems with Semi-stiff Boundary Conditions: Existence and Bubbling
Résumé
Let Ω ⊂ R2 be smooth bounded simply connected. We consider the simplified Ginzburg-Landau energy Eε(u), where u:Ω→C. We prescribe |u|=1 and deg(u,∂Ω)=1. In this setting, there are no minimizers of Eε. Using a mountain pass approach, we obtain existence, for large ε, of critical points of Eε. Our analysis relies on Wente estimates and on the analysis of bubbling phenomena for Palais-Smale sequences.
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