Mean Curvature Motion of Graphs with Constant Contact Angle at a Free Boundary

Details Mean Curvature Motion of Graphs with Constant Contact Angle at a Free Boundary Mean Curvature Motion of Graphs with Constant Contact Angle at a Free Boundary

2008-12-08

arxiv.org/abs/0812.1573v1

Mathematics

Analysis of PDEs

Revised version of the preprint with similar title posted in May 2008

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 mean curvature motion of a network of hypersurfaces with triple junctions, with constant contact angle at the junctions.

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