Optimal Transportation Problems with Free Dirichlet Regions

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Optimal transportation networks as free Dirichlet regions for the Monge-Kantorovich problem (2003, background): “In fact, we expect, as the numerical results from [5] suggest, that at least when the measures φ± are sufficiently nice (i.”
{Euclidean, metric, and Wasserstein} gradient flows: an overview (2016, methodology): “This kind of distance has also been used in [28] (inspired by [21]) to model free transport costs on other lower dimensional sets, and not only the boundary (with the goal to model, for instance, transportation networks, and optimize their shape).”
A presentation of the average distance minimizing problem (2012, background): “One can find in [4, 5, 7, 12, 14] some more detailed interpretations of Problem (1.”
Optimal Transport for Applied Mathematicians: Calculus of Variations, PDEs, and Modeling (2015, methodology): “This kind of distance has also been used in [95] (inspired by [70]) to model free transport costs on other lower dimensional sets and not only the boundary (with the goal to model, for instance, transportation networks and optimize their shape).”