The Monge–Ampère equation and its link to optimal transportation-Reference-Cited by-同舟云学术

The Monge–Ampère equation and its link to optimal transportation

Published:2014-05-16 Issue:4 Volume:51 Page:527-580
ISSN:0273-0979
Container-title:Bulletin of the American Mathematical Society
language:en
Short-container-title:Bull. Amer. Math. Soc.

Author:

De Philippis Guido,Figalli Alessio

Abstract

We survey old and new regularity theory for the Monge–Ampère equation, show its connection to optimal transportation, and describe the regularity properties of a general class of Monge–Ampère type equations arising in that context.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/bull/2014-51-04/S0273-0979-2014-01459-4/S0273-0979-2014-01459-4.pdf

Reference113 articles.

1. Balls and quasi-metrics: a space of homogeneous type modeling the real analysis related to the Monge-Ampère equation;Aimar, H.;J. Fourier Anal. Appl.,1998

2. Existence and uniqueness of a convex surface with a given integral curvature;Alexandroff, A.;C. R. (Doklady) Acad. Sci. URSS (N.S.),1942

3. Smoothness of the convex surface of bounded Gaussian curvature;Alexandroff, A.;C. R. (Doklady) Acad. Sci. URSS (N.S.),1942

4. Springer Monographs in Mathematics;Alexandrov, A. D.,2005

5. A. D. Alexandrov, Dirichlet’s problem for the equation 𝑑𝑒𝑡|𝑧ᵢⱼ|=𝜑(𝑧₁,…,𝑧_{𝑛},𝑧,𝑥₁,…,𝑥_{𝑛}) I. (Russian) Vestnik Leningrad. Univ. Ser. Mat. Meh. Astr. 13 (1958), no. 1, 5–24 .

Cited by 89 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Uniqueness when the $$L_p$$ curvature is close to be a constant for $$p\in [0,1)$$;Calculus of Variations and Partial Differential Equations;2024-06-27

2. Plugin estimation of smooth optimal transport maps;The Annals of Statistics;2024-06-01

3. Optimal Estimation of Smooth Transport Maps with Kernel SoS;SIAM Journal on Mathematics of Data Science;2024-04-15

4. On a family of fully nonlinear integrodifferential operators : from fractional Laplacian to nonlocal Monge–Ampère;Analysis & PDE;2024-02-05

5. Entire solutions to the parabolic Monge–Ampère equation with unbounded nonlinear growth in time;Nonlinear Analysis;2024-02