2014
DOI: 10.1080/03605302.2013.851214
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Minimax Critical Points in Ginzburg-Landau Problems with Semi-Stiff Boundary Conditions: Existence and Bubbling

Abstract: Let Ω ⊂ R 2 be a smooth bounded simply connected domain. We consider the simplified Ginzburg-2 , where u : Ω → C. We prescribe |u| = 1 and deg (u, ∂Ω) = 1. In this setting, there are no minimizers of E ε . Using a mountain pass approach, we obtain existence of critical points of E ε for large ε. Our analysis relies on Wente estimates and on the study of bubbling phenomena for Palais-Smale sequences.

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Cited by 21 publications
(33 citation statements)
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“…To prove the uniqueness part, we use the fact that all 0-homogeneous 1/2-harmonic maps in R 2 can be written in terms of finite Blaschke products, which are rational functions of the complex variable. This fact has been established in [30] (see also [3,9]). Using this representation, we prove rigidity among degree ±1 maps by domain deformations.…”
Section: Introductionmentioning
confidence: 52%
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“…To prove the uniqueness part, we use the fact that all 0-homogeneous 1/2-harmonic maps in R 2 can be written in terms of finite Blaschke products, which are rational functions of the complex variable. This fact has been established in [30] (see also [3,9]). Using this representation, we prove rigidity among degree ±1 maps by domain deformations.…”
Section: Introductionmentioning
confidence: 52%
“…In turn, this last identity together with (5.27) and Lemma A.1 yields 3 . Notice that F : [0, 1) → R is an increasing function, and that F (0) = 2 − 2 log(2) > 0.…”
Section: 3mentioning
confidence: 77%
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“…In Sec. 6, we present a very recent result of Berlyand, Rybalko, Sandier, and the author concerning the existence of critical points for large ε [10], while in Sec. 8, we briefly describe a work in progress with Lamy on the existence of critical points for small ε [28].…”
Section: Introductionmentioning
confidence: 93%