Minimax Critical Points in Ginzburg-Landau Problems with Semi-stiff Boundary Conditions: Existence and Bubbling - Archive ouverte HAL Access content directly
Journal Articles Communications in Partial Differential Equations Year : 2014

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

Abstract

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.
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Dates and versions

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

Identifiers

  • HAL Id : hal-00747639 , version 2

Cite

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⟩
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