On the equivalence of static and dynamic weak optimal transport
Abstract
We show that there is a PDE formulation in terms of Fokker–Planck equations for weak optimal transport problems. The main novelty is that we introduce a minimization problem involving Fokker–Planck equations in the extended sense of measure-valued solutions and prove that it is equal to the associated weak transport problem.
Fields of Study & Subjects
Markov Chains and Monte Carlo Methods
Stochastic processes and statistical mechanics
Statistical Mechanics and Entropy
Publication details
- Journal / source
- Comptes Rendus Mathématique
- Volume
- 364
- Issue
- G1
- Pages
- 205–236
- Publication date
- 17 March 2026
- Language
- EN