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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
Article

Abstract

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.

Keywords

Precise Statement Direct Proof Universal Constant Decay Estimate Local Integrability 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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