Second order stability for the Monge-Ampere equation and strong Sobolev convergence of optimal transport maps

Details Second order stability for the Monge-Ampere equation and strong Sobolev convergence of optimal transport maps Second order stability for the Monge-Ampere equation and strong Sobolev convergence of optimal transport maps

2012-02-24

arxiv.org/abs/1202.5561v2

Mathematics

Analysis of PDEs

Scientific paper

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.

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