Nonlocal-Interaction Vortices

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Abstract
We consider sequences of quadratic nonlocal functionals, depending on a small parameter [Formula: see text], that approximate the Dirichlet integral by a well-known result by Bourgain, Brezis, and Mironescu. Similarly to what is done for core-radius approximations to vortex energies in the case of the Dirichlet integral, we further scale such energies by [Formula: see text] and restrict them to [Formula: see text]-valued functions. We introduce a notion of convergence of functions to integral currents with respect to which such energies are equicoercive, and show the convergence to a vortex energy, similarly to the limit behavior of Ginzburg–Landau energies at the vortex scaling.
Funding Information
  • Università degli Studi di Sassari
  • Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni

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