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

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 W2,1 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
Volume6
Issue number4
DOIs
StatePublished - Dec 5 2013

    Fingerprint

Keywords

  • Monge-Ampère
  • Sobolev convergence
  • Stability

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Applied Mathematics

Cite this