Probabilistic representation and uniqueness results for measure-valued solutions of transport equations

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Unbalanced optimal transport: Dynamic and Kantorovich formulations (2015, unknown): “= ζ/ρ ) (see [20, Prop.”
Implicit Bias of Gradient Descent for Wide Two-layer Neural Networks Trained with the Logistic Loss (2020, unknown): “One the other hand, ν t 0 has full support on S p − 1 since it can be written as the pushforward of a rescaled version of ν 0 by a diﬀeomorphism, see Maniglia (2007, Eq.”
Transport Equation and Cauchy Problem for Non-Smooth Vector Fields (2008, background): “d |bt| p dµtdt 1, in Theorem 8.2.1 of [12], see also [ 70 ] for the extension to the case p = 1 and to the non-homogeneous continuity equation.”
Finite volume schemes for the approximation via characteristics of linear convection equations with irregular data (2011, background): “Works that are related to the framework of measures are [7, 8, 6, 14, 5].”
Continuity equations and ODE flows with non-smooth velocity* (2014, background): “1 of [16], see also [89] for the extension to the case p = 1 and to the non-homogeneous continuity equation.”
Existence, Uniqueness, Stability and Differentiability Properties of the Flow Associated to Weakly Differentiable Vector Fields (2009, background): “See also Maniglia [111] for an extension to the non homogeneous case.”