Lorentz Space Estimates for the Ginzburg-Landau Energy

  title={Lorentz Space Estimates for the Ginzburg-Landau Energy},
  author={Sylvia Serfaty and Ian Tice},
In this paper we prove novel lower bounds for the Ginzburg-Landau energy with or without magnetic field. These bounds rely on an improvement of the “vortex balls construction” estimates by extracting a new positive term in the energy lower bounds. This extra term can be conveniently estimated through a Lorentz space norm, on which it thus provides an upper bound. The Lorentz space L2,∞ we use is critical with respect to the expected vortex profiles and can serve to estimate the total number of… CONTINUE READING

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