Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

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
MathSciNet review: 2465662
Retrieve article in: PDF

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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 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 at the origin.

References:

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