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arXiv · 2309.10112

Topological singularities arising from fractional-gradient energies

Roberto Alicandro·Andrea Braides·Margherita Solci·Giorgio Stefani
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Abstract

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.

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Roberto Alicandro, Andrea Braides, Margherita Solci, Giorgio Stefani. 2023-09-18. Topological singularities arising from fractional-gradient energies. https://arxiv.org/abs/2309.10112

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