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In this paper, we continue the study of Lorentz space estimates for the Ginzburg-Landau energy started in [15]. We focus on getting estimates for the Ginzburg-Landau energy with external magnetic field h  ex  in certain interesting regimes of h  ex . This allows us to show that for configurations close to minimizers or local minimizers of the energy, the vorticity mass of the configuration (u, A) is comparable to the L 2, ∞ Lorentz space norm of ∇ A  u. We also establish convergence of the gauge-invariant Jacobians (vorticity measures) in the dual of a function space defined in terms of Lorentz spaces.

Lorentz space estimates and Jacobian convergence for the Ginzburg-Landau energy with applied magnetic field