Mathematische Annalen

, Volume 357, Issue 1, pp 11–22 | Cite as

A note on interior \(W^{2,1+ \varepsilon }\)estimates for the Monge–Ampère equation

  • G. De Philippis
  • A. FigalliEmail author
  • O. Savin


By a variant of the techniques introduced by the first two authors in De Philippis and Figalli (Invent Math 2012) to prove that second derivatives of solutions to the Monge–Ampère equation are locally in \(L\log L\), we obtain interior \(W^{2,1+\varepsilon }\) estimates.


Precise Statement Direct Proof Universal Constant Decay Estimate Local Integrability 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Scuola Normale Superiore di PisaPisaItaly
  2. 2.Department of MathematicsThe University of Texas at Austin AustinUSA
  3. 3.Department of MathematicsColumbia UniversityNew YorkUSA

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