On Monge-Ampere equations with homogeneous right hand side
Analysis of PDEs
2007-06-27 v1
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.
Cite
@article{arxiv.0706.3748,
title = {On Monge-Ampere equations with homogeneous right hand side},
author = {Pangiota Daskalopoulos and Ovidiu Savin},
journal= {arXiv preprint arXiv:0706.3748},
year = {2007}
}