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Journal of the American Mathematical Society

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ISSN 1088-6834 (online) ISSN 0894-0347 (print)

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Pointwise $C^{2,\alpha }$ estimates at the boundary for the Monge-Ampère equation
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by O. Savin
J. Amer. Math. Soc. 26 (2013), 63-99
Published electronically: August 7, 2012


We prove a localization property of boundary sections for solutions to the Monge-Ampère equation. As a consequence we obtain pointwise $C^{2,\alpha }$ estimates at boundary points under appropriate local conditions on the right-hand side and boundary data.
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Bibliographic Information
  • O. Savin
  • Affiliation: Department of Mathematics, Columbia University, New York, New York 10027
  • MR Author ID: 675185
  • Email:
  • Received by editor(s): January 28, 2011
  • Received by editor(s) in revised form: January 5, 2012
  • Published electronically: August 7, 2012
  • Additional Notes: The author was partially supported by NSF grant 0701037.
  • © Copyright 2012 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 26 (2013), 63-99
  • MSC (2010): Primary 35J96
  • DOI:
  • MathSciNet review: 2983006