Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New estimates on the regularity of the pressure in density-constrained
  Mean Field Games   We consider variational Mean Field Games endowed with a constraint on the
maximal density of the distribution of players. Minimizers of the variational
formulation are equilibria for a game where both the running cost and the final
cost of each player is augmented by a pressure effect, i.e. a positive cost
concentrated on the set where the density saturates the constraint. Yet, this
pressure is a priori only a measure and regularity is needed to give a precise
meaning to its integral on trajectories. We improve, in the limited case where
the Hamiltonian is quadratic, which allows to use optimal transport techniques
after time-discretization, the results obtained in a paper of the second author
with Cardaliaguet and M{\'e}sz{\'a}ros. We prove H1 and L infinity regularity
under very mild assumptions on the data, and explain the consequences for the
MFG, in terms of the value function and of the Lagrangian equilibrium
formulation.

19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph