We prove that a reaction-diffusion inclusion provides a sub-optimal approximation for anisotropic motion by mean curvature in the nonsmooth case. This result is valid in any space dimension and with a time-dependent driving force, provided we assume the existence of a regular flow. The crystalline case is included. As a by-product of our analysis, a comparison theorem between regular flows is obtained. This result implies uniqueness of the original flow.
Approximation and comparison for nonsmooth anisotropic motion by mean curvature in R^N
NOVAGA, MATTEO
2000
Abstract
We prove that a reaction-diffusion inclusion provides a sub-optimal approximation for anisotropic motion by mean curvature in the nonsmooth case. This result is valid in any space dimension and with a time-dependent driving force, provided we assume the existence of a regular flow. The crystalline case is included. As a by-product of our analysis, a comparison theorem between regular flows is obtained. This result implies uniqueness of the original flow.
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