Second order stability for the Monge-Ampere equation and strong Sobolev convergence of optimal transport maps
classification
🧮 math.AP
keywords
convergeequationhandmapsmonge-ampereoptimalrightside
read the original abstract
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.
This paper has not been read by Pith yet.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.