Mean Curvature Motion of Graphs with Constant Contact Angle and Moving Boundaries

Details Mean Curvature Motion of Graphs with Constant Contact Angle and Moving Boundaries Mean Curvature Motion of Graphs with Constant Contact Angle and Moving Boundaries

2008-05-29

arxiv.org/abs/0805.4592v1

Mathematics

Analysis of PDEs

54 pages

Scientific paper

We consider the motion by mean curvature of an $n$-dimensional graph over a time-dependent domain in $\mathbb{R}^n$, intersecting $\mathbb{R}^n$ at a constant angle. In the general case, we prove local existence for the corresponding quasilinear parabolic equation with a free boundary, and derive a continuation criterion based on the second fundamental form. If the initial graph is concave, we show this is preserved, and that the solution exists only for finite time. This corresponds to a symmetric version of triple junction motion of hypersurfaces by mean curvature, with constant angles at the junction.

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