English

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"