Second order stability for the Monge-Ampere equation and strong Sobolev convergence of optimal transport maps (1202.5561v3)

Published 24 Feb 2012 in math.AP

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.

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