Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Sobolev regularity of mass transport and transportation inequalities   We study Sobolev a priori estimates for the optimal transportation $T =
\nabla \Phi$ between probability measures $\mu=e^{-V} \ dx$ and $\nu=e^{-W} \
dx$ on $\R^d$. Assuming uniform convexity of the potential $W$ we show that
$\int \| D^2 \Phi\|^2_{HS} \ d\mu$, where $\|\cdot\|_{HS}$ is the
Hilbert-Schmidt norm, is controlled by the Fisher information of $\mu$. In
addition, we prove similar estimate for the $L^p(\mu)$-norms of $\|D^2 \Phi\|$
and obtain some $L^p$-generalizations of the well-known Caffarelli contraction
theorem. We establish a connection of our results with the Talagrand
transportation inequality. We also prove a corresponding dimension-free version
for the relative Fisher information with respect to a Gaussian measure.

31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat