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arXiv · 1908.03697

Gradient estimates for the Allen-Cahn equation on Riemannian manifolds

Songbo Hou
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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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Songbo Hou. 2019-08-10. Gradient estimates for the Allen-Cahn equation on Riemannian manifolds. https://arxiv.org/abs/1908.03697

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