Abstract
In this paper, we prove Souplet-Zhang type gradient estimates for a nonlinear parabolic equation on smooth metric measure spaces with the compact boundary under the Dirichlet boundary condition when the Bakry-Emery Ricci tensor and the weighted mean curvature are both bounded below. As an application, we obtain a new Liouville type result for some space-time functions on such smooth metric measure spaces. These results generalize previous linear equations to a nonlinear case.
Acknowledgment
The authors thank the anonymous referee for making useful comments and pointing out some errors in an earlier version of the paper. This work was partially supported by the Natural Science Foundation of Shanghai (17ZR1412800).
Citation
Xuenan Fu. Jia-Yong Wu. "Gradient estimates for a nonlinear parabolic equation with Dirichlet boundary condition." Kodai Math. J. 45 (1) 96 - 109, March 2022. https://doi.org/10.2996/kmj/kmj45106
Information
