Generic level sets in mean curvature flow are BV solutions

T Laux, A Ullrich - arXiv preprint arXiv:2301.01097, 2023 - arxiv.org
T Laux, A Ullrich
arXiv preprint arXiv:2301.01097, 2023arxiv.org
We show that a generic levelset of the viscosity solution to mean curvature flow is a
distributional solution in the framework of sets of finite perimeter by Luckhaus and
Sturzenhecker, which in addition saturates the optimal energy dissipation rate. This extends
the fundamental work of Evans and Spruck (J. Geom. Anal. 1995), which draws a similar
connection between the viscosity solution and Brakke flows.
We show that a generic levelset of the viscosity solution to mean curvature flow is a distributional solution in the framework of sets of finite perimeter by Luckhaus and Sturzenhecker, which in addition saturates the optimal energy dissipation rate. This extends the fundamental work of Evans and Spruck (J. Geom. Anal. 1995), which draws a similar connection between the viscosity solution and Brakke flows.
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