Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On duality principles for non-convex optimization with applications to
  superconductivity and some existence results for a model in non-linear
  elasticity   This article develops duality principles applicable to the Ginzburg-Landau
system in superconductivity. The main results are obtained through standard
tools of convex analysis, functional analysis, calculus of variations and
duality theory. In the second section, we present the general result for the
case including a magnetic field and the respective magnetic potential in a
local extremal context. Finally, in the last section we develop some global
existence results for a model in elasticity.

18
The categories of this paper are: econ
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph