Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A family of functional inequalities: Lojasiewicz inequalities and
  displacement convex functions   For displacement convex functionals in the probability space equip\-ped with
the Monge-Kantorovich metric we prove the equivalence between the gradient and
functional type \L oja\-sie\-wicz inequalities. \chg{We also discuss the more
general case of $\lambda$-convex functions and we provide a general convergence
theorem for the corresponding gradient dynamics. Specialising our results to
the Boltzmann entropy, we recover Otto-Villani's theorem asserting the
equivalence between logarithmic Sobolev and Talagrand's inequalities. The
choice of power-type entropies shows a new equivalence between
Gagliardo-Nirenberg inequality and a nonlinear Talagrand inequality. Some
nonconvex results and other types of equivalences are discussed.

27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci