Pointwise 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

MathSciNet review:
2983006

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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 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

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.