Analysis & PDE
- Anal. PDE
- Volume 3, Number 4 (2010), 359-407.
Mean curvature motion of graphs with constant contact angle at a free boundary
We consider the motion by mean curvature of an -dimensional graph over a time-dependent domain in intersecting 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.
Anal. PDE, Volume 3, Number 4 (2010), 359-407.
Received: 8 December 2008
Revised: 8 October 2009
Accepted: 17 October 2009
First available in Project Euclid: 20 December 2017
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Freire, Alexandre. Mean curvature motion of graphs with constant contact angle at a free boundary. Anal. PDE 3 (2010), no. 4, 359--407. doi:10.2140/apde.2010.3.359. https://projecteuclid.org/euclid.apde/1513731094