English

Mean curvature flow with obstacles

Numerical Analysis 2015-06-03 v2

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.

Keywords

Cite

@article{arxiv.1111.5141,
  title  = {Mean curvature flow with obstacles},
  author = {Luís Almeida and Antonin Chambolle and Matteo Novaga},
  journal= {arXiv preprint arXiv:1111.5141},
  year   = {2015}
}

Comments

18 pages

R2 v1 2026-06-21T19:39:44.253Z