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
Article Dans Une Revue Communications in Partial Differential Equations Année : 2014

Minimax Critical Points in Ginzburg-Landau Problems with Semi-stiff Boundary Conditions: Existence and Bubbling

Résumé

Let $\Omega\subset{\mathbb R}^2$ be smooth bounded simply connected. We consider the simplified Ginzburg-Landau energy $E_\varepsilon (u)$, where $u:\Omega\to{\mathbb C}$. On the boundary, we prescribe $|u|=1$ and deg$\, (u, \partial\Omega)=1$. In this setting, there are no minimizers of $E_\varepsilon$. Using a mountain pass approach, we obtain existence, for large $\varepsilon$, of critical points of $E_\varepsilon$. Our analysis relies on Wente estimates and on the analysis of bubbling phenomena for Palais-Smale sequences.
Fichier principal
Vignette du fichier
bmrs_20130826.pdf (372.04 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

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

Identifiants

  • HAL Id : hal-00747639 , version 2

Citer

Leonid Berlyand, Petru Mironescu, Volodymyr Rybalko, Etienne Sandier. Minimax Critical Points in Ginzburg-Landau Problems with Semi-stiff Boundary Conditions: Existence and Bubbling. Communications in Partial Differential Equations, 2014, 39 (5), pp.946-1005. ⟨hal-00747639v2⟩
466 Consultations
383 Téléchargements

Partager

Gmail Facebook X LinkedIn More