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Implicit time discretization of the mean curvature flow with a discontinuous forcing term. (English) Zbl 1170.65054
The authors study the minimizing movements method (implicit time discretization) for anisotropic mean curvature flow with a discontinuous forcing term. It is shown that the implicit time discretization is consistent with sub- and superflows associated with the evolution equation under consideration. This result is then used to prove convergence to a weak solution which, under certain assumptions, is contained in the zero level set of the viscosity solution.

MSC:
65K10 Numerical optimization and variational techniques
49Q05 Minimal surfaces and optimization
49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games
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