Gradient estimates for mean curvature flow with Neumann boundary conditions
Analysis of PDEs
2021-12-22 v6
Abstract
We study the mean curvature flow of graphs both with Neumann boundary conditions and transport terms. We derive boundary gradient estimates for the mean curvature flow. As an application, the existence of the mean curvature flow of graphs is presented. A key argument is a boundary monotonicity formula of a Huisken type derived using reflected backward heat kernels. Furthermore, we provide regularity conditions for the transport terms.
Keywords
Cite
@article{arxiv.1512.03886,
title = {Gradient estimates for mean curvature flow with Neumann boundary conditions},
author = {Masashi Mizuno and Keisuke Takasao},
journal= {arXiv preprint arXiv:1512.03886},
year = {2021}
}
Comments
21 pages, 3 figures, Accepted for publication in "NoDEA. Nonlinear Differential Equations and Applications"