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
DOI:
https://doi.org/10.1090/S0894-0347-2012-00747-4
Published electronically:
August 7, 2012
MathSciNet review:
2983006
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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
MR Author ID:
675185
Email:
savin@math.columbia.edu
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.
