We introduce and study a new optimal transport problem on a bounded domain \({{\bar{\Omega }}}\subset {\mathbb {R}}^d\), 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 \({{\bar{\Omega }}}\) on the one hand, and on the other hand between two independent optimal transport problems set on \(\Omega \) and \({\partial \Omega }\).

中文翻译：

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具有体积/界面相互作用和流量罚分的新运输距离

我们介绍并研究了通过动态Benamou–Brenier公式定义的有界域\（{{\ bar {\ Omega}}} \子集{\ mathbb {R}} ^ d \}上的新的最优输运问题。该模型以不同方式处理内部和边界上的运动，并惩罚了两者之间的质量传递。所得的距离一方面在\（{{bar {\ Omega}}} \）上的经典最优输运之间进行插值，另一方面在\（\ Omega \）和\（ {\ partial \ Omega} \）。