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.
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