Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal Controlled Transports with Free End Times Subject to
  Import/Export Tariffs   We analyze controlled mass transportation plans with free end-time that
minimize the transport cost induced by the generating function of a Lagrangian
within a bounded domain, in addition to costs incurred as export and import
tariffs at entry and exit points on the boundary. We exhibit a dual variational
principle \`a la Kantorovich, that takes into consideration the additional
tariffs. We then show that the primal optimal transport problem has an
equivalent Eulerian formulation whose dual involves the resolution of a
Hamilton-Jacobi-Bellman quasi-variational inequality with non-homogeneous
boundary conditions. This allows us to prove existence and to describe the
solutions for both the primal optimization problem and its Eulerian
counterpart.

3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-th
16
The categories of this paper are: stat
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The categories of this paper are: hep-lat
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys