Integral Estimates for Transport Densities

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Optimal Transport for Applied Mathematicians: Calculus of Variations, PDEs, and Modeling (2015, background): “The proofs are essentially taken from [273]: previous results, through very different techniques, were first presented in [144, 146, 145].”
Absolute continuity and summability of transport densities: simpler proofs and new estimates (2009, background): “without passing through the theory of σ −tangential gradient (see for instance [8, 14 ]).”
Sharp summability for Monge Transport density via Interpolation (2004, methodology): “To prove the theorem, we first of all recall the known results we use, the regularity results proved in [5, 6] and the Marcinkievicz interpolation result, which can be found for example in [10].”
Free boundaries in optimal transport and Monge-Ampere obstacle problems (2010, background): “This is illustrated by the following simple example, which also indicates why new hypotheses are required to ensure uniqueness. principle have been examined extensively in the context of dynamical problems since the work of Otto [65] and Jordan, Kinderlehrer and Otto [50], see also e.g. Agueh [2], A”
The Monge problem for strictly convex norms in Rd (2010, background): “The transport density plays a crucial role in the proof of existence given in [17], and good estimates from above are available for σγ [1, 15, 14, 16].”