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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

Pointwise $ C^{2,\alpha}$ estimates at the boundary for the Monge-Ampère equation


Author: O. Savin
Journal: J. Amer. Math. Soc. 26 (2013), 63-99
MSC (2010): Primary 35J96
Published electronically: August 7, 2012
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Abstract: 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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Additional Information

O. Savin
Affiliation: Department of Mathematics, Columbia University, New York, New York 10027
Email: savin@math.columbia.edu

DOI: http://dx.doi.org/10.1090/S0894-0347-2012-00747-4
PII: S 0894-0347(2012)00747-4
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.
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.