Analysis & PDE

  • Anal. PDE
  • Volume 3, Number 4 (2010), 359-407.

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

Alexandre Freire

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We consider the motion by mean curvature of an n-dimensional graph over a time-dependent domain in n intersecting 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.

Article information

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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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K55: Nonlinear parabolic equations 53C44: Geometric evolution equations (mean curvature flow, Ricci flow, etc.)

mean curvature flow triple junctions free boundaries


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.

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