Demonstrates equivalence between weak optimal transport and Fokker-Planck formulations, implying new insights into transport theory.
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.
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Bohdan Bulanyi (2026) studied this question.
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