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Global $ W^{2,p}$ estimates for the Monge-Ampère equation


Author: O. Savin
Journal: Proc. Amer. Math. Soc. 141 (2013), 3573-3578
MSC (2010): Primary 35J96
DOI: https://doi.org/10.1090/S0002-9939-2013-11748-X
Published electronically: July 1, 2013
MathSciNet review: 3080179
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Abstract: We use a localization property of boundary sections for solutions to the Monge-Ampère equation and obtain global $ W^{2,p}$ estimates under natural assumptions on the domain 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: https://doi.org/10.1090/S0002-9939-2013-11748-X
Received by editor(s): March 4, 2011
Received by editor(s) in revised form: January 5, 2012
Published electronically: July 1, 2013
Additional Notes: The author was partially supported by NSF grant 0701037.
Communicated by: James E. Colliander
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.