no. 5
Mean curvature flow with obstacles
Annales de l'I.H.P. Analyse non linéaire, Volume 29 (2012) no. 5, pp. 667-681

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.

DOI: 10.1016/j.anihpc.2012.03.002
Classification: 35R37, 35R45, 49J40, 49Q20, 53A10
Keywords: Obstacle problem, Mean curvature flow, Minimizing movements 
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     title = {Mean curvature flow with obstacles},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
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Almeida, L.; Chambolle, A.; Novaga, M. Mean curvature flow with obstacles. Annales de l'I.H.P. Analyse non linéaire, Volume 29 (2012) no. 5, pp. 667-681. doi: 10.1016/j.anihpc.2012.03.002

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