Accepted Paper

Inserted: 24 feb 2012
Last Updated: 30 oct 2017

Journal: Anal. PDE
Year: 2012

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.

Keywords: optimal transportation, stability, Monge-Ampère equation

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