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Smoothness of radial solutions to Monge-Ampère equations

Author(s): Cristian Rios; Eric T. Sawyer
Journal: Proc. Amer. Math. Soc. 137 (2009), 1373-1379.
MSC (2000): Primary 35B65, 35J70; Secondary 35D05, 35D10, 35C15
Posted: November 5, 2008
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Abstract: We prove that generalized convex radial solutions to the generalized Monge-Ampère equation $ \det D^2u = f(\vert x\vert^2/2,u,\vert\nabla u\vert^2/2)$ with $ f$ smooth are always smooth away from the origin. Moreover, we characterize the global smoothness of these solutions in terms of the order of vanishing of $ f $ at the origin.

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Additional Information:

Cristian Rios
Affiliation: Department of Mathematics, University of Calgary, Calgary, Alberta, Canada
Email: crios@math.ucalgary.ca

Eric T. Sawyer
Affiliation: Department of Mathematics, McMaster University, Hamilton, Ontario, Canada
Email: saw6453cdn@aol.com

DOI: 10.1090/S0002-9939-08-09694-9
PII: S 0002-9939(08)09694-9
Received by editor(s): April 22, 2008
Posted: November 5, 2008
Communicated by: Matthew J. Gursky
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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