W2,1 regularity for solutions of the Monge-Ampère equation

Guido de Philippis, Alessio Figalli

Research output: Contribution to journalArticlepeer-review


In this paper we prove that a strictly convex Alexandrov solution u of the Monge-Ampère equation, with right-hand side bounded away from zero and infinity, is W2,1loc. This is obtained by showing higher integrability a priori estimates for D2u, namely D2u∈LlogkL for any k∈ℕ.

Original languageEnglish (US)
Pages (from-to)55-69
Number of pages15
JournalInventiones Mathematicae
Issue number1
StatePublished - Apr 2013

ASJC Scopus subject areas

  • General Mathematics


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