A new transportation distance with bulk/interface interactions and flux penalization
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS(2021)
摘要
We introduce and study a new optimal transport problem on a bounded domain Ω̅⊂ℝ^d , defined via a dynamical Benamou–Brenier formulation. The model handles differently the motion in the interior and on the boundary, and penalizes the transfer of mass between the two. The resulting distance interpolates between classical optimal transport on Ω̅ on the one hand, and on the other hand between two independent optimal transport problems set on Ω and ∂Ω .
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关键词
Dynamical optimal transport,Benamou–Brenier formulations,Unbalanced optimal transport,Wasserstein distance,Wasserstein–Fisher–Rao metric,Coupled Hamilton–Jacobi equations,Bulk/interface interaction
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