Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Monge problem with vanishing gradient penalization: Vortices and
  asymptotic profile   We investigate the approximation of the Monge problem (minimizing
\int\_$\Omega$ |T (x) -- x| d$\mu$(x) among the vector-valued maps T with
prescribed image measure T \# $\mu$) by adding a vanishing Dirichlet energy,
namely $\epsilon$ \int\_$\Omega$ |DT |^2. We study the $\Gamma$-convergence as
$\epsilon$ $\rightarrow$ 0, proving a density result for Sobolev (or Lipschitz)
transport maps in the class of transport plans. In a certain two-dimensional
framework that we analyze in details, when no optimal plan is induced by an H
^1 map, we study the selected limit map, which is a new "special" Monge
transport, possibly different from the monotone one, and we find the precise
asymptotics of the optimal cost depending on $\epsilon$, where the leading term
is of order $\epsilon$| log $\epsilon$|.

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The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio