Calculus of Variations and Geometric Measure Theory
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L. Almeida - A. Chambolle - M. Novaga

Mean curvature flow with obstacles

created by novaga on 21 Nov 2011
modified on 07 Jan 2016


Published Paper

Inserted: 21 nov 2011
Last Updated: 7 jan 2016

Journal: Annales IHP - Analyse Nonlineaire
Volume: 29
Pages: 667-681
Year: 2012


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.


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