부산대학교 도서관

We consider sequences of quadratic nonlocal functionals, depending on a small parameter ε, 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 (log ε)-1 and restrict them to S¹-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. [ABSTRACT FROM AUTHOR]