Second Order Stability for the Monge-ampère Equation and Strong Sobolev Convergence of Optimal Transport Maps
نویسنده
چکیده
The aim of this note is to show that Alexandrov solutions of the Monge-Ampère 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 Lloc. As a corollary we deduce strong W 1,1 loc stability of optimal transport maps.
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