Second order stability for the Monge–Ampère equation and strong Sobolev convergence of optimal transport maps
- 21 August 2013
- journal article
- Published by Mathematical Sciences Publishers in Analysis & PDE
- Vol. 6 (4) , 993-1000
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 W2,1loc if their right hand side converge strongly in L1loc. As a corollary we deduce strong W1,1loc stability of optimal transport mapsKeywords
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