Mean curvature motion of graphs with constant contact angle at a free boundary

Alexandre Freire
2010 Analysis & PDE  
We consider the motion by mean curvature of an n-dimensional graph over a time-dependent domain in ‫ޒ‬ n intersecting ‫ޒ‬ 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
more » ... version of mean curvature motion of a network of hypersurfaces with triple junctions with constant contact angle at the junctions. w t = 1 + |Dw| 2 H MSC2000: 35K55, 53C44. -3840 is published continuously online. Periodical rate postage paid at Berkeley, CA 94704, and additional mailing offices. APDE peer review and production are managed by EditFLOW ™ from Mathematical Sciences Publishers. PUBLISHED BY mathematical sciences publishers
doi:10.2140/apde.2010.3.359 fatcat:362rn3y6fjasdch723g2xy2ssi