Gradient estimates for mean curvature flow with Neumann boundary conditions

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.

21 pages, 3 figures, Accepted for publication in "NoDEA. Nonlinear Differential Equations and Applications"

References in corpus (2)

• Convergence of the Allen-Cahn equation with Neumann boundary conditions
• Mean curvature flow with free boundary outside a hypersphere

Cited by in corpus (2)

• Level-set forced mean curvature flow with the Neumann boundary condition
• A curve shortening equation with time-dependent mobility related to grain boundary motions