Gradient estimates for the Allen-Cahn equation on Riemannian manifolds
arXiv:1908.03697
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.
11 pages