On the equivalence of static and dynamic weak optimal transport
arXiv:2311.13872 · doi:10.5802/crmath.814
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.
arXiv commentMinor corrections, 29 pages. To appear in Comptes Rendus Mathématique