Brakke’s inequality for the thresholding scheme

Tim Bastian Laux and Felix Otto

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Submission date: 14. Aug. 2017
Pages: 24
published in: Calculus of variations and partial differential equations, 59 (2020) 1, art-no. 39 
DOI number (of the published article): 10.1007/s00526-020-1696-8
Bibtex
MSC-Numbers: 35A15, 65M12, 74N20
Keywords and phrases: Mean curvature flow, thresholding, MBO, diffusion generated motion
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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 Esedoğlu 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.