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

Leonid Berlyand, Petru Mironescu, Volodymyr Rybalko, Etienne Sandier

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

Let Ω ⊂ ℝ2 be a smooth bounded simply connected domain. We consider the simplified Ginzburg-Landau energy (Formula Presented), where u: Ω → ℂ. We prescribe {pipe}u{pipe} = 1 and deg (u, ∂Ω) = 1. In this setting, there are no minimizers of E ε{lunate}. Using a mountain pass approach, we obtain existence of critical points of E ε{lunate} for large ε{lunate}. Our analysis relies on Wente estimates and on the study of bubbling phenomena for Palais-Smale sequences.

Original languageEnglish (US)
Pages (from-to)946-1005
Number of pages60
JournalCommunications in Partial Differential Equations
Volume39
Issue number5
DOIs
StatePublished - May 2014

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Minimax Critical Points in Ginzburg-Landau Problems with Semi-Stiff Boundary Conditions: Existence and Bubbling'. Together they form a unique fingerprint.

Cite this