Research
Main research interests
Calculus of Variations,
Optimal Transport,
Degenerate elliptic PDEs,
Evolution equations, gradient flows, population dynamics,
Equilibrium problems, Game Theory, economical applications,
Numerics and approximation
Papers, on the CVGMT
website
List of publications (updated
October 2017)
Most recent topics
-
Fundamental theory of optimal transport (transport plans, densities,
potentials, existence and regularity of transport maps)
-
Branched Transport Structures
variational formulations and model, regularity
Landscape functions and applications to river basins
elliptic approximation via Modica-Mortola and numerics
-
Mean Field Games: variational formulation, regularity, density
constraints
new: L∞ estimates in variational MFG
-
Incompressible Euler equations à la Brenier
-
Gradient flows in Wasserstein spaces
Density-constrained PDEs for crowd motion
new: estimates for Keller-Segel equations
new: BV and Sobolev estimates for the JKO scheme
-
Moment measures: variational methods based on transport theory, numerics
-
Traffic Congestion in continuous settings
-
Models for the urban planning and for the equilibrium of residential and service areas
-
Minimization under length constraints and Steiner problem
new: elliptic approximation for connected networks
Main, most recent, and regular collaborators
(excluding the works I did with my PhD students, see the dedicated page)
Lorenzo Brasco (Ferrara)
Giuseppe Buttazzo
(Pisa)
Pierre
Cardaliaguet (Dauphine)
Guillaume
Carlier (Dauphine)
José Antonio
Carrillo de La Plata (Imperial)
Gigi De Pascale (Firenze)
Simone Di Marino (INDAM-SNS)
Chloé Jimenez (Brest)
Antoine
Lemenant (Paris 7)
Gabriel Peyré (CNRS-ENS)
Bertrand Maury (Orsay)
Jean-Michel Morel (ENS Cachan)
Aude Roudneff-Chupin (formerly Orsay)
Xu-Jia Wang
(Canberra)
Qinglan Xia (UC Davis)