Mean curvature flow with obstacles

Luís Almeida (1) , Antonin Chambolle (2) , Matteo Novaga (3)

1 LJLL - Laboratoire Jacques-Louis Lions
2 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
3 Dipartimento di Matematica [Pisa]

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.

Mots clés: obstacle problem; mean curvature flow; minimizing movements

Domaines: Analyse numérique [cs.NA]

Luís Almeida, Antonin Chambolle, Matteo Novaga. Mean curvature flow with obstacles. Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2012, 29 (5), pp.667 - 681. ⟨10.1016/j.anihpc.2012.03.002⟩. ⟨hal-00643453v2⟩