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arXiv · 2112.06165

Gradient estimates for a nonlinear parabolic equation with Dirichlet boundary condition

Xuenan Fu·Jia-Yong Wu
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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.

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Xuenan Fu, Jia-Yong Wu. 2021-12-12. Gradient estimates for a nonlinear parabolic equation with Dirichlet boundary condition. https://doi.org/10.2996/kmj/kmj45106

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