Gradient estimates for the Allen-Cahn equation on Riemannian manifolds

Published 10 Aug 2019 in math.DG and math.AP | (1908.03697v1)

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

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