On Monge-Ampere equations with homogeneous right hand side

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We study the regularity and behavior at the origin of solutions to the two-dimensional degenerate Monge-Ampere equation with homogeneous right hand side of degree alpha, alpha>-2. We show that when alpha > 0, solutions admit only two possible behaviors near the origin, radial and non-radial. We also show that the radial behavior is unstable. For alpha<0 we prove that solutions admit only the radial behavior near the origin.

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Analysis of PDEs, 35J70

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http://salesiana.dossiersoluciones.com/handle/123456789/132444

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0706.3748
 http://arxiv.org/abs/0706.3748

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arXiv