Calculus of Variations and Geometric Measure Theory

X. Lamy - E. Marconi

Stability of the vortex in micromagnetics and related models

created by marconi on 16 Sep 2022



Inserted: 16 sep 2022
Last Updated: 16 sep 2022

Year: 2022


We consider line-energy models of Ginzburg-Landau type in a two-dimensional simply connected bounded domain. Con gurations of vanishing energy have been characterized by Jabin, Otto and Perthame: the domain must be a disk, and the con guration a vortex. We prove a quantitative version of this statement in the class of $C^{1,1}$ domains, improving on previous results by Lorent. In particular, the deviation of the domain from a disk is controlled by a power of the energy, and that power is optimal. The main tool is a Lagrangian representation introduced by the second author, which allows to decompose the energy along characteristic curves.