Topological singularities arising from fractional-gradient energies

2023/09/18 by Alicandro, Roberto, Braides, Andrea, Solci, Margherita +1 · 2 citations
#46E35 #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary 49J45. Secondary 35Q56

paper · doi:10.48550/arxiv.2309.10112

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, Γ-converge to vortex-type energies with respect to the flat convergence of Jacobians. The compactness and the Γ-\liminf follow by comparison with standard Ginzburg-Landau functionals depending on Riesz potentials. The Γ-\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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