Gradient estimates for a nonlinear parabolic equation with Dirichlet boundary condition
Differential Geometry
2022-08-16 v1 Analysis of PDEs
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.
Cite
@article{arxiv.2112.06165,
title = {Gradient estimates for a nonlinear parabolic equation with Dirichlet boundary condition},
author = {Xuenan Fu and Jia-Yong Wu},
journal= {arXiv preprint arXiv:2112.06165},
year = {2022}
}
Comments
12 pages, accepted by Kodai Math. J