Gradient estimates for the Allen-Cahn equation on Riemannian manifolds
Differential Geometry
2019-08-13 v1 Analysis of PDEs
Abstract
In this paper, we consider bounded positive solutions to the Allen-Cahn equation on complete noncompact Riemannian manifolds without boundary. We derive gradient estimates for those solutions. As an application, we get a Liouville type theorem on manifolds with nonnegative Ricci curvature.
Keywords
Cite
@article{arxiv.1908.03697,
title = {Gradient estimates for the Allen-Cahn equation on Riemannian manifolds},
author = {Songbo Hou},
journal= {arXiv preprint arXiv:1908.03697},
year = {2019}
}
Comments
11 pages