Second order stability for the Monge–Ampère equation and strong Sobolev convergence of optimal transport maps
Second order stability for the Monge–Ampère equation and strong Sobolev convergence of optimal transport maps
复制标题
Monge-Ampère 方程的二阶稳定性和最优输运图的强 Sobolev 收敛
DOI：
--
复制
发表时间：
2012
期刊：
影响因子：
--
通讯作者：
A. Figalli
中科院分区：
文献类型：
--
作者：
G. Philippis;A. Figalli
本文的目的是证明Monge-Ampere方程的Alexandrov解，当其右端在零和无穷远处有界时，当其右端在L1中强收敛时，Alexandrov解在W2，1中强收敛.作为推论，我们得到了最优迁移映射的强W^{1，1}_{loc}$稳定性.
The aim of this note is to show that Alexandrov solutions of the Monge-Ampere equation, with right hand side bounded away from zero and infinity, converge strongly in $W^{2,1}_{loc}$ if their right hand side converge strongly in $L^1_{loc}$. As a corollary we deduce strong $W^{1,1}_{loc}$ stability of optimal transport maps.