For linear control systems satisfying a generalized Kalman rank condition, the static optimal transport cost equals the dynamic Benamou-Brenier cost for every p>1, with minimizers in both problems.
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On the equivalence between static and dynamic optimal transport governed by linear control systems
For linear control systems satisfying a generalized Kalman rank condition, the static optimal transport cost equals the dynamic Benamou-Brenier cost for every p>1, with minimizers in both problems.