Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global-in-time regularity via duality for congestion-penalized Mean
  Field Games   After a brief introduction to one of the most typical problems in Mean Field
Games, the congestion case (where agents pay a cost depending on the density of
the regions they visit), and to its variational structure, we consider the
question of the regularity of the optimal solutions. A duality argument, used
for the first time in a paper by Y. Brenier on incompressible fluid mechanics,
and recently applied to MFG with density constraints, allows to easily get some
Sobolev regularity, locally in space and time. In the paper we prove that a
careful analysis of the behaviour close to the final time allows to extend the
same result including t = T .

29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph