On Monge–Kantorovich problem in the plane

Comptes Rendus Mathematique - Tập 348 - Trang 267-271 - 2010
Yinfang Shen1,2, Weian Zheng1,2
1SFS, ITCS, East China Normal University, Shanghai, China, 200062
2Department of Mathematics, University of California, Irvine, CA 92697, USA

Tài liệu tham khảo

L. Ambrosio, Optimal transport maps in Monge–Kantorovich problem, in: Proceedings of ICM, Beijing 2002, vol. iii, 2002, pp. 131–140 Brenier, 1987, Décomposition polaire et réarrangement monotone des champs de vecteurs, C. R. Acad. Sci. Paris, Ser. I Math., 305, 805 Brenier, 1991, Polar factorization and monotone rearrangement of vector-valued functions, Comm. Pure Appl. Math., 44, 375, 10.1002/cpa.3160440402 L. Caffarelli, Nonlinear elliptic theory and the Monge–Ampere equation, in: Proc. ICM, vol. i, 2002, pp. 179–187 Evans, 1999, Differential equations methods for the Monge–Kantorovich mass transfer problem, Mem. Amer. Math. Soc., 137 Gilbarg, 1983 Rachev, 1998, Mass Transportation Problems, vol I: Theory Rachev, 1998, Mass Transportation Problems, vol. II: Applications N. Trudinger, Recent developments in elliptic partial differential equations of Monge–Ampère type, in: Proc. ICM, 2006, invited lecture