Mean curvature flow with obstacles

Details Mean curvature flow with obstacles Mean curvature flow with obstacles

2011-11-22

arxiv.org/abs/1111.5141v2

Mathematics

Numerical Analysis

18 pages

Scientific paper

We consider the evolution of fronts by mean curvature in the presence of obstacles. We construct a weak solution to the flow by means of a variational method, corresponding to an implicit time-discretization scheme. Assuming the regularity of the obstacles, in the two-dimensional case we show existence and uniqueness of a regular solution before the onset of singularities. Finally, we discuss an application of this result to the positive mean curvature flow.

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