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 W2,1loc if their right-hand sides converge strongly in L1loc. As a corollary, we deduce strong W1,1loc stability of optimal transport maps.
Second order stability for the Monge–Ampère equation and strong Sobolev convergence of optimal transport maps
Figalli, Alessio;De Philippis, Guido
2013
Abstract
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 W2,1loc if their right-hand sides 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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