English

On the equivalence of static and dynamic weak optimal transport

Optimization and Control 2026-03-23 v3 Analysis of PDEs Probability

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.

Keywords

Cite

@article{arxiv.2311.13872,
  title  = {On the equivalence of static and dynamic weak optimal transport},
  author = {Bohdan Bulanyi},
  journal= {arXiv preprint arXiv:2311.13872},
  year   = {2026}
}

Comments

Minor corrections, 29 pages. To appear in Comptes Rendus Math\'ematique