Brakke's inequality for the thresholding scheme

Tim Laux; Felix Otto

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arXiv · 1708.03071

Brakke's inequality for the thresholding scheme

Tim Laux·Felix Otto

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Abstract

We continue our analysis of the thresholding scheme from the variational viewpoint and prove a conditional convergence result towards Brakke's notion of mean curvature flow. Our proof is based on a localized version of the minimizing movements interpretation of Esedo\u{g}lu and the second author. We apply De Giorgi's variational interpolation to the thresholding scheme and pass to the limit in the resulting energy-dissipation inequality. The result is conditional in the sense that we assume the time-integrated energies of the approximations to converge to those of the limit.

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Tim Laux, Felix Otto. 2017-08-10. Brakke's inequality for the thresholding scheme. https://arxiv.org/abs/1708.03071

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