Mean Curvature Motion of Triple Junctions of Graphs in Two Dimensions

Details Mean Curvature Motion of Triple Junctions of Graphs in Two Dimensions Mean Curvature Motion of Triple Junctions of Graphs in Two Dimensions

2008-09-03

arxiv.org/abs/0809.0636v1

Mathematics

Analysis of PDEs

31 pages, submitted

Scientific paper

We consider a system of three surfaces, graphs over a bounded domain in ${\mathbb R}^2$, intersecting along a time-dependent curve and moving by mean curvature while preserving the pairwise angles at the curve of intersection (equal to $2\pi/3$.) For the corresponding two-dimensional parabolic free boundary problem we prove short-time existence of classical solutions (in parabolic H\"{o}lder spaces), for sufficiently regular initial data satisfying a compatibility condition.

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