Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local regularity for mean-field games in the whole space   In this paper, we investigate the Sobolev regularity for mean-field games in
the whole space $\Rr^d$. This is achieved by combining integrability for the
solutions of the Fokker-Planck equation with estimates for the Hamilton-Jacobi
equation in Sobolev spaces. To avoid the mathematical challenges posed due to
the lack of compactness, we prove an entropy dissipation estimate for the
adjoint variable. This, together with the non-linear adjoint method, yields
uniform estimates for solutions of the Hamilton-Jacobi equation in
$W^{1,p}_{loc}(\Rr^d)$.

22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph