Abstract
We establish the interior gradient estimate for general 1-D anisotropic curvature flow. The estimate depends only on the height of the graph and not on the gradient at initial time. The proof relies on the monotonicity property of the number of zeros for the parabolic equation.
Highlights
We establish the interior gradient estimate for general 1-D anisotropic curvature flow
One direction to extend those results are to consider general anisotropic curvature problem, namely, to consider the variational problem corresponding to the energy functional
If one allows the interior gradient estimate to depend on the gradient at t = 0, the argument of [7] gives the interior gradient estimate
Summary
Abstract: We establish the interior gradient estimate for general 1-D anisotropic curvature flow. One direction to extend those results are to consider general anisotropic curvature problem, namely, to consider the variational problem corresponding to the energy functional We show the interior gradient estimates for general anisotropic curvature flow for one-dimensional case which is independent of the initial time gradient.
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