A new transportation distance between non-negative measures, with applications to gradients flows with Dirichlet boundary conditions

122 citations recorded by the source corpus.

Citations in the corpus

Optimal Transport for Applied Mathematicians: Calculus of Variations, PDEs, and Modeling (2015, unknown): “On the other hand, standard Hilbertian results on the heat equation can provide uniqueness for this equation, as the authors underlined in [165].”
Generalized Wasserstein Distance and its Application to Transport Equations with Source (2012, unknown): “We now recall the distance Wb2 defined in [8].”
A new optimal transport distance on the space of finite Radon measures (2015, unknown): “Recently, some efforts [23, 40, 41] were made to construct new optimal transport distances between measures with different masses, and some non-mass preserving reaction-diffusion systems were interpreted as gradient flows [14, 33].”
{Euclidean, metric, and Wasserstein} gradient flows: an overview (2016, unknown): “Anyway, we see that Dirichlet conditions do not find their translation into W2 gradient flows! To cope with Dirichlet boundary conditions, Figalli and Gigli defined in [44] a sort of modified Wasserstein distance, with a special role played by the boundary ∂Ω, in order to study the Heat equation ∂t̺”