JournalsaihpcVol. 29, No. 5pp. 667–681

Mean curvature flow with obstacles

  • L. Almeida

    CNRS, UMR 7598, Laboratoire Jacques-Louis Lions, France, UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, France

  • A. Chambolle

    CMAP, Ecole Polytechnique, CNRS, France

  • M. Novaga

    Dip. di Matematica, Università di Padova, via Trieste 63, 35121 Padova, Italy
Mean curvature flow with obstacles cover
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Abstract

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. 667–681

DOI 10.1016/J.ANIHPC.2012.03.002