Mean curvature flow with obstacles
arXiv:1111.5141 · doi:10.1016/j.anihpc.2012.03.002
Abstract
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.
arXiv comment18 pages