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

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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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     author = {Almeida, L. and Chambolle, A. and Novaga, M.},
     title = {Mean curvature flow with obstacles},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {667--681},
     publisher = {Elsevier},
     volume = {29},
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     year = {2012},
     doi = {10.1016/j.anihpc.2012.03.002},
     mrnumber = {2971026},
     zbl = {1252.49072},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2012.03.002/}
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Almeida, L.; Chambolle, A.; Novaga, M. Mean curvature flow with obstacles. Annales de l'I.H.P. Analyse non linéaire, Tome 29 (2012) no. 5, pp. 667-681. doi: 10.1016/j.anihpc.2012.03.002

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