论文标题
带有散装/接口相互作用和通量惩罚的新运输距离
A new transportation distance with bulk/interface interactions and flux penalization
论文作者
论文摘要
我们介绍并研究了通过动态的benamou-brenier公式定义的有限域$ \barΩ\ subset \ mathbb r^d $上的新的最佳传输问题。该模型对内部和边界上的运动进行不同的处理，并惩罚两者之间的质量转移。一方面，在$ \barΩ$上的经典最佳传输之间以及在两个独立的最佳运输问题与$ω$和$ \ partialω$之间的距离之间的距离。
We introduce and study a new optimal transport problem on a bounded domain $\barΩ\subset \mathbb R^d$, 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 $\barΩ$ on the one hand, and on the other hand between two independent optimal transport problems set on $Ω$ and $\partial Ω$.
