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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Regularity of subelliptic Monge-Ampère equations in the plane


Authors: Pengfei Guan and Eric Sawyer
Journal: Trans. Amer. Math. Soc. 361 (2009), 4581-4591
MSC (2000): Primary 35J60, 35B65
Published electronically: April 14, 2009
MathSciNet review: 2506420
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Abstract: We establish a $ C^\infty$ regularity result for $ C^{1,1}$ solutions of degenerate Monge-Ampère equation in $ \mathbb{R}^2$, under the assumption that the trace of the Hessian is bounded from below.


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Additional Information

Pengfei Guan
Affiliation: Department of Mathematics and Statistics, McGill University, Montreal, Quebec, Canada H3A 2K6
Email: guan@math.mcgill.ca

Eric Sawyer
Affiliation: Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada L8S 4K1
Email: sawyer@mcmaster.ca

DOI: http://dx.doi.org/10.1090/S0002-9947-09-04640-6
PII: S 0002-9947(09)04640-6
Received by editor(s): April 26, 2007
Published electronically: April 14, 2009
Additional Notes: Research of the authors was supported in part by NSERC Discovery Grants.
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.