RT Monograph
SR 00
A1 Blanchet, Adrien
A1 Bolte, Jérôme
T1 A family of functional inequalities
YR 2017
FD 2017-03
VO 17-66
SP 11
AB For displacement convex functionals in the probability space equipped with the Monge-Kantorovich metric we prove the equivalence between the gradient and functional type Lojasiewicz inequalities. In a second part, we specialise these inequalities to some classical geodesically convex functionals. For the Boltzmann entropy, we obtain the equivalence between logarithmic Sobolev and Talagrand's inequalities. On the other hand, the non-linear entropy and the Gagliardo-Nirenberg inequality provide a Talagrand inequality which seems to be a new equivalence. Our method allows also to recover some results on the asymptotic behaviour of the associated gradient flows.
T2 IAST Working Paper
PB IAST Working Paper
PP Toulouse
AV Published
LK https://publications.ut-capitole.fr/id/eprint/26149/
UL http://iast.fr/pub/31597