Gradient estimates for the Allen-Cahn equation on Riemannian manifolds

Hou, Songbo

doi:10.1090/proc/14324

Gradient estimates for the Allen-Cahn equation on Riemannian manifolds
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Proc. Amer. Math. Soc. 147 (2019), 619-628 Request permission

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.

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