Comptes Rendus
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On the equivalence of static and dynamic weak optimal transport
[Sur l’équivalence du transport optimal faible statique et dynamique]
Bohdan Bulanyi1 orcid
1Université catholique de Louvain, Institut de Recherche en Mathématique et Physique, Chemin du Cyclotron 2 bte L7.01.01, 1348 Louvain-la-Neuve, Belgium
Comptes Rendus. Mathématique, Volume 364 (2026), pp. 205-236

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.

Nous montrons qu’il existe une formulation EDP en termes d’équations de Fokker–Planck pour des problèmes de transport optimal faible. La principale nouveauté est que nous introduisons un problème de minimisation dont la contrainte est constituée des équations de Fokker–Planck pour les mesures générales et prouvons qu’il est égal au problème de transport optimal faible correspondant.

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Révisé le :
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DOI : 10.5802/crmath.814
Classification : 49Q22, 28A33, 49J45, 49N15, 49Q20
Keywords: Fokker–Planck equation, weak transport problem, duality, Laplace operator, Green function, subharmonic function, viscosity solution, Hamilton–Jacobi–Bellman equation
Mots-clés : Équation de Fokker–Planck, transport optimal généralisé, dualité, opérateur de Laplace, fonction de Green, fonction sous-harmonique, solutions de viscosité, équation de Hamilton–Jacobi–Bellman

Bohdan Bulanyi  1

1 Université catholique de Louvain, Institut de Recherche en Mathématique et Physique, Chemin du Cyclotron 2 bte L7.01.01, 1348 Louvain-la-Neuve, Belgium
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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     title = {On the equivalence of static and dynamic weak optimal transport},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {205--236},
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     volume = {364},
     doi = {10.5802/crmath.814},
     language = {en},
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Bohdan Bulanyi. On the equivalence of static and dynamic weak optimal transport. Comptes Rendus. Mathématique, Volume 364 (2026), pp. 205-236. doi: 10.5802/crmath.814

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