Minimax Critical Points in Ginzburg-Landau Problems with Semi-stiff Boundary Conditions: Existence and Bubbling - Laboratoire d'Analyse et de Mathématiques Appliquées Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2012

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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Dates et versions

hal-00747639 , version 1 (31-10-2012)
hal-00747639 , version 2 (29-08-2013)

Identifiants

  • HAL Id : hal-00747639 , version 1

Citer

Leonid Berlyand, Petru Mironescu, Volodymyr Rybalko, Etienne Sandier. Minimax Critical Points in Ginzburg-Landau Problems with Semi-stiff Boundary Conditions: Existence and Bubbling. 2012. ⟨hal-00747639v1⟩
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