Asymptotics for minimizers of the Ginzburg–Landau energy with optimal regularity of the boundary data and applications

Laurain, Paul; Petrides, Romain

Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 33 (2024) no. 5, pp. 1251-1295

We perform the classical asymptotic analysis for the Ginzburg–Landau energy which originates from the celebrated paper by Bethuel, Brezis, Hélein for nonsmooth boundary data. More precisely, we give optimal regularity assumptions on the boundary curve of planar domains and Dirichlet boundary data on them. When the Dirichlet boundary data is the tangent vector field of the boundary curve, our framework allows us to define a natural energy minimizing frame for simply connected domains enclosing Weil–Petersson curves.

Nous effectuons l’analyse asymptotique classique pour l’énergie de Ginzburg–Landau provenant du célèbre papier de Bethuel, Brezis, Hélein pour des données non lisses au bord. Plus précisément, nous donnons des hypothèses optimales de régularité sur la courbe qui borde le domaine plan et sur la condition de Dirichlet. Quand la donnée de Dirichlet est le champ de vecteur unitaire tangent de la courbe du bord, notre travail permet de définir un repère mobile d’énergie minimale sur les domaines simplement connexes bordés par une courbe Weil–Petersson.

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