Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A perturbative approach to the parabolic optimal transport problem for
  non-MTW costs   Fix a pair of smooth source and target densities $\rho$ and $\rho^*$ of equal
mass, supported on bounded domains $\Omega, \Omega^* \subset \mathbb{R}^n$.
Also fix a cost function $c_0 \in C^{4,\alpha}(\overline{\Omega} \times
\overline{\Omega^*})$ satisfying the weak regularity criterion of Ma,
Trudinger, and Wang, and assume $\Omega$ and $\Omega^*$ are uniformly $c_0$-
and $c_0^*$-convex with respect to each other. We consider a parabolic version
of the optimal transport problem between $(\Omega,\rho)$ and
$(\Omega^*,\rho^*)$ when the cost function $c$ is a sufficiently small $C^4$
perturbation of $c_0$, and where the size of the perturbation depends on the
given data. Our main result establishes global-in-time existence of a solution
$u \in C^2_xC^1_t(\overline\Omega \times [0, \infty))$ of this parabolic
problem, and convergence of $u(\cdot,t)$ as $t \to \infty$ to a Kantorovich
potential for the optimal transport map between $(\Omega,\rho)$ and
$(\Omega^*,\rho^*)$ with cost function $c$. A noteworthy aspect of our work is
that $c$ does \emph{not} necessarily satisfy the weak Ma-Trudinger-Wang
condition.

1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an