L. Ambrosio and W. Gangbo, Hamiltonian ODEs in the Wasserstein space of probability measures, Communications on Pure and Applied Mathematics, vol.47, issue.1, pp.18-53, 2008.
DOI : 10.1002/cpa.20188

L. Ambrosio, N. Gigli, and G. Savaré, Gradient Flows: In Metric Spaces and in the Space of Probability Measures, 2008.

J. Benamou and Y. Brenier, A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem, Numerische Mathematik, vol.84, issue.3, pp.375-393, 2000.
DOI : 10.1007/s002110050002

R. M. Dudley, Real Analysis and Probability, 2002.
DOI : 10.1017/CBO9780511755347

L. C. Evans and R. F. Gariepy, Measure Theory and Fine Properties of Functions, 1992.

G. Monge, Mémoire sur la théorie des déblais et de remblais Histoire de l'Académie Royale des Sciences de Paris, pp.666-704

B. Piccoli and F. Rossi, Transport Equation with Nonlocal Velocity in Wasserstein Spaces: Convergence of Numerical Schemes, Acta Applicandae Mathematicae, vol.54, issue.1, pp.73-105, 2013.
DOI : 10.1007/s10440-012-9771-6

B. Piccoli and F. Rossi, Generalized Wasserstein distance and its application to transport equations with source, Archive for Rational Mechanics and Analysis, pp.335-358, 2014.
DOI : 10.1007/s00205-013-0669-x
URL : http://arxiv.org/abs/1206.3219

R. T. Rockafellar, Conjugate duality and optimization, Conference Board of Math. Sciences Series, SIAM Publications, 1974.
DOI : 10.1137/1.9781611970524
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.298.6548

C. Villani, Optimal Transport: Old and New, Grundlehren der mathematischen Wissenschaften, 2008.
DOI : 10.1007/978-3-540-71050-9

C. Villani, Topics in Optimal Transportation, Graduate Studies in Mathematics, vol.58, 2003.
DOI : 10.1090/gsm/058