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 maps.
Second order stability for the Monge-Ampere equation and strong Sobolev convergence of Optimal Transport Maps
De Philippis, Guido;
2013-01-01
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 maps.File in questo prodotto:
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2013_Second Order Stability For The Monge?Ampe?re Equation And Strong Sobolev Convergence Of Optimal Transport Maps.pdf
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