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

On Monge-Ampere equations with homogeneous right hand side