Abstract
We investigate the parabolic Allen-Cahn equation
under general geometric flow on complete noncompact manifolds. We first prove a local gradient estimate for the positive solution to this equation, then we obtain a Harnack inequality as an application.
Citation
Zhengchao Ji. Liang Zhao. "Gradient estimates for a nonlinear elliptic equation under geometric flow." Rocky Mountain J. Math. 51 (5) 1681 - 1690, October 2021. https://doi.org/10.1216/rmj.2021.51.1681
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