TY - JOUR
T1 - Minimax Critical Points in Ginzburg-Landau Problems with Semi-Stiff Boundary Conditions
T2 - Existence and Bubbling
AU - Berlyand, Leonid
AU - Mironescu, Petru
AU - Rybalko, Volodymyr
AU - Sandier, Etienne
N1 - Funding Information:
The work of LB was supported by NSF grant DMS-1106666. The work of VR was partially supported by NSF grant DMS-1106666. PM was supported by the ANR project ANR-12-BS01-0013-03.
PY - 2014/5
Y1 - 2014/5
N2 - 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.
AB - 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.
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U2 - 10.1080/03605302.2013.851214
DO - 10.1080/03605302.2013.851214
M3 - Article
AN - SCOPUS:84897377438
SN - 0360-5302
VL - 39
SP - 946
EP - 1005
JO - Communications in Partial Differential Equations
JF - Communications in Partial Differential Equations
IS - 5
ER -