English

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}
}
R2 v1 2026-06-21T08:42:02.790Z