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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Abstract

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

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

Dates
Received: 8 December 2008
Revised: 8 October 2009
Accepted: 17 October 2009
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.apde/1513731094

Digital Object Identifier
doi:10.2140/apde.2010.3.359

Mathematical Reviews number (MathSciNet)
MR2718258

Zentralblatt MATH identifier
1228.35126

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

Keywords
mean curvature flow triple junctions free boundaries

Citation

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


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