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.
- Publication:
-
arXiv e-prints
- Pub Date:
- November 2023
- DOI:
- arXiv:
- arXiv:2311.13872
- Bibcode:
- 2023arXiv231113872B
- Keywords:
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- Mathematics - Optimization and Control;
- Mathematics - Analysis of PDEs;
- Mathematics - Probability;
- 49Q22;
- 28A33;
- 49J45;
- 49N15;
- 49Q20
- E-Print:
- 28 pages. The motivation, topic of the paper and connections with literature have been amended. Improved main result