135 citations · 273 across the 17 of their papers we have counts for
15 papers · 1 filter
A family of functional inequalities: Lojasiewicz inequalities and displacement convex functions
Jérôme Bolte, Adrien Blanchet
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 Łoja\-si…
Topological interactions in a Boltzmann-type framework
Adrien Blanchet, Pierre Degond
We consider a finite number of particles characterised by their positions and velocities. At random times a randomly chosen particle, the follower, adopts the velocity of another p…
A hybrid variational principle for the Keller-Segel system in
Adrien Blanchet, José A. Carrillo, David Kinderlehrer +3
We construct weak global in time solutions to the classical Keller-Segel system cell movement by chemotaxis in two dimensions when the total mass is below the well-known critical v…
From Nash to Cournot-Nash equilibria via the Monge-Kantorovich problem
Adrien Blanchet, Guillaume Carlier
The notion of Nash equilibria plays a key role in the analysis of strategic interactions in the framework of player games. Analysis of Nash equilibria is however a complex issu…
Optimal transport and Cournot-Nash equilibria
Adrien Blanchet, Guillaume Carlier
We study a class of games with a continuum of players for which Cournot-Nash equilibria can be obtained by the minimisation of some cost, related to optimal transport. This cost is…
The parabolic-parabolic Keller-Segel system with critical diffusion as a gradient flow in $\RR^d$,
Adrien Blanchet, Philippe Laurençot
It is known that, for the parabolic-elliptic Keller-Segel system with critical porous-medium diffusion in dimension $\RR^d$, (also referred to as the quasilinear Smolucho…