Calculus of Variations and Geometric Measure Theory

B. Bulanyi

On the equivalence of static and dynamic weak optimal transport

created by bulanyi on 30 Dec 2024

[BibTeX]

Submitted Paper

Inserted: 30 dec 2024
Last Updated: 30 dec 2024

Year: 2024

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


Download: