Research
Main research interests
Calculus of Variations,
Optimal Transport,
Shape Optimization,
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 July 2015)
Problems
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Fundamental theory of optimal transport (transport plans, densities,
potentials, existence and regularity of transport maps)
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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: regularity of the pressure in a density-constrained MFG
-
Incompressible Euler equations à la Brenier
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Gradient flows in Wasserstein spaces
Density-constrained PDEs for crowd motion
new: estimates for Keller-Segel equations
new: BV estimates for the JKO scheme
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Traffic Congestion in continuous settings
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Optimal locations of facilities
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Models for the urban planning and for the equilibrium of residential and service areas
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Minimization under length constraints and Steiner problem
new: elliptic approximation for connected networks
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Compliance optimization
Main, most recent, and regular collaborators
(excluding current and recent PhD students of mine, see the dedicated page)
Fethallah Benmansour (formerly EPFL)
Adrien
Blanchet (Toulouse 1)
Alessio Brancolini Muenster)
Lorenzo Brasco (Marseille)
Giuseppe Buttazzo
(Pisa)
Pierre
Cardaliaguet (Dauphine)
Guillaume Carlier (Dauphine)
Gigi De Pascale (Pisa)
Chloé Jimenez (Brest)
Antoine
Lemenant (Paris 7)
Bertrand Maury (Orsay)
Jean-Michel Morel (ENS Cachan)
Pascal Mossay (Newcastle)
Edouard Oudet
(Grenoble)
Gabriel
Peyré (CNRS + Dauphine)
Aude
Roudneff-Chupin (formerly Orsay)
Eugene Stepanov (St. Petersburg + Pisa)
Xu-Jia Wang (Canberra)