Implicit time discretization of the mean curvature flow with a discontinuous forcing term.

Antonin Chambolle (1) , Matteo Novaga (2)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 Dipartimento di Matematica Pura e Applicata [Padova]

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.

Mots clés: Mean curvature flow; Implicit discretization; Stochastic mean curvature flow

Domaines: Analyse numérique [math.NA]

Antonin Chambolle, Matteo Novaga. Implicit time discretization of the mean curvature flow with a discontinuous forcing term.. Interfaces and Free Boundaries : Mathematical Analysis, Computation and Applications, 2008, 10 (3), pp.283--300. ⟨hal-00381471⟩