Calculus of Variations and Geometric Measure Theory

A. Chambolle - M. Novaga

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

created by novaga on 27 Jul 2005
modified on 10 Nov 2018


Published Paper

Inserted: 27 jul 2005
Last Updated: 10 nov 2018

Journal: Interfaces and Free Boundaries
Volume: 10
Pages: 283-300
Year: 2008


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.