Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lorentz Space Estimates and Jacobian Convergence for the Ginzburg-Landau
  Energy with Applied Magnetic Field   In this paper we continue the study of Lorentz space estimates for the
Ginzburg-Landau energy started in our previous paper, \cite{p1}. 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
$L^{2,\infty}$ Lorentz space norm of $\nabla_A u$. We also establish
convergence of the gauge-invariant Jacobians (vorticity measures) in the dual
of a function space defined in terms of Lorentz spaces.

31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs