The Distribution of Superconductivity Near a Magnetic Barrier

@article{Assaad2019TheDO,
  title={The Distribution of Superconductivity Near a Magnetic Barrier},
  author={W. Assaad and Ayman Kachmar and Mikael Persson-Sundqvist},
  journal={Communications in Mathematical Physics},
  year={2019},
  volume={366},
  pages={269-332}
}
We consider the Ginzburg–Landau functional, defined on a two-dimensional simply connected domain with smooth boundary, in the situation when the applied magnetic field is piecewise constant with a jump discontinuity along a smooth curve. In the regime of large Ginzburg–Landau parameter and strong magnetic field, we study the concentration of the minimizing configurations along this discontinuity by computing the energy of the minimizers and their weak limit in the sense of distributions. 
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TLDR
An accurate asymptotic formula is determined for the minimize energy of the Ginzburg-Landau functional and it is shown that the energy minimizers have vortices.
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