Geodesic
Implicit time discretization of the mean curvature flow with a discontinuous forcing term
Antonin Chambolle1 orcid ; Matteo Novaga2 orcid
1Ecole Polytechnique, Palaiseau, France
2Università di Pisa, Italy
Interfaces and free boundaries, Tome 10 (2008) no. 3, pp. 283-300

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DOI

We consider an implicit time discretization for the motion of a hypersurface driven by its anisotropic mean curvature. We prove some convergence results of the scheme under very general assumptions on the forcing term, which include in particular the case of a typical path of the Brownian motion. We compare this limit with other available solutions, whenever they are defined. As a by-product of the analysis, we also provide a simple proof of the coincidence of the limit flow with the regular evolutions, defined for small times, in the case of a regular forcing term.
DOI : 10.4171/ifb/190
Classification : 35-XX, 65-XX, 76-XX, 92-XX

Antonin Chambolle  1   ; Matteo Novaga  2

1 Ecole Polytechnique, Palaiseau, France
2 Università di Pisa, Italy 
Antonin Chambolle; Matteo Novaga. Implicit time discretization of the mean curvature flow with a discontinuous forcing term. Interfaces and free boundaries, Tome 10 (2008) no. 3, pp. 283-300. doi: 10.4171/ifb/190
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