4 papers
Path-Space Optimal Transport with Interactions: Kinetic Equations and Eikonal Structure
Rene Cabrera
We study a dynamical optimal transport problem on path-space with kinetic cost and nonlocal interaction. For a Gaussian interaction kernel, cyclical monotonicity and the regularity…
A minimax Bilinear Transport Problem and Nash-Monge-Kantorovich Maps
Rene Cabrera, Edward Huynh
We study a min-max bilinear transport problem arising from a two-player zero-sum game with quadratic kinetic and interaction costs. Starting from a dynamic path space formulation,…
Regularization estimates of the Landau-Coulomb diffusion
Rene Cabrera, Maria Gualdani, Nestor Guillen
The Landau-Coulomb equation is an important model in plasma physics featuring both nonlinear diffusion and reaction terms. In this manuscript we focus on the diffusion operator wit…
An optimal transportation principle for interacting paths and congestion
Rene Cabrera
In this work we study a modification of the Monge-Kantorovich problem taking into account path dependence and interaction effects between particles. We prove existence of solutions…