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hal-00643453, version 1

Mean curvature flow with obstacles

Luís Almeida 1, Antonin Chambolle (, http://www.cmap.polytechnique.fr/~antonin) 2, Matteo Novaga () 3

(2011-11-20)

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.

  • 1:  Laboratoire Jacques-Louis Lions (LJLL)
  • CNRS : UMR7598 – Université Pierre et Marie Curie [UPMC] - Paris VI
  • 2:  Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP)
  • Polytechnique - X – CNRS : UMR7641
  • 3:  Dipartimento di Matematica Pura ed Applicata
  • Università degli studi di Padova
  • Domain : Mathematics/Numerical Analysis
  • Keywords : obstacle problem – mean curvature flow – minimizing movements
  • Comment : 18 pages
  • Available versions :  v1 (2011-11-22) v2 (2012-03-20)
 
  • hal-00643453, version 1
  • http://hal.archives-ouvertes.fr/hal-00643453
  • oai:hal.archives-ouvertes.fr:hal-00643453
  • From: Antonin Chambolle <>
  • Submitted on: Monday, 21 November 2011 22:44:53
  • Updated on: Tuesday, 22 November 2011 10:49:09