Second order stability for the monge-ampère equation and strong sobolev convergence of optimal transport maps

Guido De Philippis, Alessio Figalli

Research output: Contribution to journalArticle


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 W2,1 loc if their right-hand sides converge strongly in L1 loc. As a corollary, we deduce strong W1,1 loc stability of optimal transport maps.

Original languageEnglish (US)
Pages (from-to)993-1000
Number of pages8
JournalAnalysis and PDE
Issue number4
StatePublished - Dec 5 2013



  • Monge-Ampère
  • Sobolev convergence
  • Stability

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Applied Mathematics

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