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arXiv · 2111.14717

Existence of Ginzburg-Landau minimizers with optimal boundary data and applications

PAul Laurain·Romain Petrides
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Abstract

We perform the classical Ginzburg-Landau analysis originated from the celebrated paper by Bethuel, Brezis, H\'elein for optimal 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.

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PAul Laurain, Romain Petrides. 2021-11-29. Existence of Ginzburg-Landau minimizers with optimal boundary data and applications. https://arxiv.org/abs/2111.14717

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