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- W2034292401 abstract "Let Ω be a smooth bounded simply connected domain in R2. We investigate the existence of critical points of the energy Eε(u)=1/2∫Ω|∇u|2+1/(4ε2)∫Ω(1−|u|2)2, where the complex map u has modulus one and prescribed degree d on the boundary. Under suitable nondegeneracy assumptions on Ω, we prove existence of critical points for small ε. More can be said when the prescribed degree equals one. First, we obtain existence of critical points in domains close to a disk. Next, we prove that critical points exist in “most” of the domains. Soit Ω un domaine borné lisse simplement connexe de R2. On édutdie l'existence de points critiques de l'énergie Eε(u)=1/2∫Ω|∇u|2+1/(4ε2)∫Ω(1−|u|2)2, où u est une fonction à valeurs complexes, dont la trace au bord est de module un et de degré prescrit d. Sous des hypothèses appropriées de non dégénérescence sur Ω, on démontre l'existence de points critiques pour ε petit. Dans le cas où le degré prescrit est égal à un, on peut préciser ce résultat. Premièrement, on obtient l'existence de points critiques dans tout domaine proche d'un disque. De plus, on démontre qu'il existe des points critiques dans la « plupart » des domaines." @default.
- W2034292401 created "2016-06-24" @default.
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- W2034292401 date "2014-08-01" @default.
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- W2034292401 title "Existence of critical points with semi-stiff boundary conditions for singular perturbation problems in simply connected planar domains" @default.
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- W2034292401 doi "https://doi.org/10.1016/j.matpur.2013.11.014" @default.
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