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arXiv · 0706.3748

On Monge-Ampere equations with homogeneous right hand side

Pangiota Daskalopoulos·Ovidiu Savin
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Abstract

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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Pangiota Daskalopoulos, Ovidiu Savin. 2007-06-26. On Monge-Ampere equations with homogeneous right hand side. https://arxiv.org/abs/0706.3748

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