5 papers
Nonlinear kinetic Fokker-Planck equations as gradient flows of the free energy
Giovanni Brigati, Guillaume Carlier, Jean Dolbeault +1
We consider nonhomogeneous kinetic equations that involve a free transport operator and a diffusion of porous medium type acting on velocities. The main novelty is a gradient flow…
The fundamental solution of a nonlinear kinetic Fokker-Planck equation
Giovanni Brigati, Guillaume Carlier, Jean Dolbeault
This paper is devoted to a fundamental solution of a nonlinear kinetic equation involving a porous medium or fast diffusion operator acting on velocities. Such a nonlinearity has i…
Weak optimal transport with moment constraints: constraint qualification, dual attainment and entropic regularization
Guillaume Carlier, Hugo Malamut, Maxime Sylvestre
We consider weak optimal problems (possibly entropically penalized) incorporating both soft and hard (including the case of the martingale condition) moment constraints. Even in th…
On a class of adversarial classification problems which admit a continuous solution
Guillaume Carlier, Maxime Sylvestre
We consider a class of adversarial classification problems in the form of zero-sum games between a classifier and an adversary. The latter is able to corrupt data, at the expense o…
Well-posedness and convergence of entropic approximation of semi-geostrophic equations
Guillaume Carlier, Hugo Malamut
We prove existence and uniqueness of solutions for an entropic version of the semi-geostrophic equations. We also establish convergence to a weak solution of the semi-geostrophic e…