Topological singularities arising from fractional-gradient energies

期刊论文
发表日期：

2025年8月1日

查看全文

Roberto Alicandro,
Andrea Braides,
Margherita Solci,
Giorgio Stefani

摘要

We prove that, on a planar regular domain, suitably scaled functionals of Ginzburg–Landau type, given by the sum of quadratic fractional Sobolev seminorms and a penalization term vanishing on the unitary sphere, \(\Gamma \) -converge to vortex-type energies with respect to the flat convergence of Jacobians. The compactness and the \(\Gamma \) - \(\liminf \) follow by comparison with standard Ginzburg–Landau functionals depending on Riesz potentials. The \(\Gamma \) - \(\limsup \) , instead, is achieved via a direct argument by joining a finite number of vortex-like functions suitably truncated around the singularity.