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.
Cite this article
L. Almeida, A. Chambolle, M. Novaga, Mean curvature flow with obstacles. Ann. Inst. H. Poincaré Anal. Non Linéaire 29 (2012), no. 5, pp. 667–681DOI 10.1016/J.ANIHPC.2012.03.002