no. 4
Approximation of parabolic equations using the Wasserstein metric
ESAIM: Modélisation mathématique et analyse numérique, Tome 33 (1999) no. 4, pp. 837-852 
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     author = {Kinderlehrer, David and Walkington, Noel J.},
     title = {Approximation of parabolic equations using the {Wasserstein} metric},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {837--852},
     year = {1999},
     publisher = {EDP Sciences},
     volume = {33},
     number = {4},
     mrnumber = {1726488},
     zbl = {0936.65121},
     language = {en},
     url = {https://www.numdam.org/item/M2AN_1999__33_4_837_0/}
}
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Kinderlehrer, David; Walkington, Noel J. Approximation of parabolic equations using the Wasserstein metric. ESAIM: Modélisation mathématique et analyse numérique, Tome 33 (1999) no. 4, pp. 837-852. https://www.numdam.org/item/M2AN_1999__33_4_837_0/

[1] J. Benamou and Y. Brenier, A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem. Preprint (1998). | Zbl

[2] J. Benamou and Y. Brenier, Weak existence for the semigeostrophic equations formulated as a coupled Monge-Ampere transport problem. SIAM J. AppL Math. 58 (1998) 1450-1461. | Zbl | MR

[3] Y. Brenier, Polar factorization and monotone rearrangement of vector-valued functions. Comm. Pure Appl. Math. 44 (1991)375-417. | Zbl | MR

[4] P.G. Ciarlet, Introduction to Numerical Linear Algebra and Optimisation. Cambridge University Press, Cambridge (1988). | Zbl | MR

[5] W.E. and F. Otto, Thermodynamically driven incompressible fluid mixtures. J. Chem. Phys. 107 (1998) 10177-10184. | Zbl

[6] M. Frechet, Sur la distance de deux lois de probabilité. C.R. Acad. Sci. 244 (1957) 689-692. | Zbl | MR

[7] W. Gangbo and A. Sweich, Optimal maps for the multidimensional Monge-Kantorovich problem. CPAM 51 (1998) 23-45. | Zbl | MR

[8] W. Gango and R.J. Mccann, The geometry of optimal transportation. Acta Math, 177 (1996) 113-161. | Zbl | MR

[9] R. Jordan, D. Kinderlehrer and F. Otto, The variational formulation of the Fokker-Planck équation. SIAM J. Math. Anal. 29 (1998) 1-17. | Zbl | MR

[10] R. Jordan, D. Kinderlehrer and F. Otto, Dynamics of the Fokker-Planck equation. Phase Transitions (to appear).

[11] E.H. Lieb and M. Loss, Analysis, Vol. 14 of Graduate Studies in Mathematics. AMS (1997). | Zbl | MR

[12] F. Otto, Dynamics of labyrinthine pattern formation in magnetic fluids. Arch. Rational Mech. Anal. 141 (1998) 63-103. | Zbl | MR

[13] N.G. Van Kampen, Stochastic Processes in Physics and Chemistry. North-Holland (1981). | Zbl | MR