Published Paper
Inserted: 30 dec 2024
Last Updated: 24 mar 2026
Journal: Comptes Rendus Mathématique
Year: 2026
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.
Keywords: viscosity solution, Laplace operator, duality, Fokker-Planck equation, weak transport problem, Green function, subharmonic function, Hamilton-Jacobi-Bellman equation
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