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arXiv · 2101.11663

De Giorgi's inequality for the thresholding scheme with arbitrary mobilities and surface tensions

Tim Laux·Jona Lelmi
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Abstract

We provide a new convergence proof of the celebrated Merriman-Bence-Osher scheme for multiphase mean curvature flow. Our proof applies to the new variant incorporating a general class of surface tensions and mobilities, including typical choices for modeling grain growth. The basis of the proof are the minimizing movements interpretation of Esedo\u{g}lu and Otto and De Giorgi's general theory of gradient flows. Under a typical energy convergence assumption we show that the limit satisfies a sharp energy-dissipation relation.

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Tim Laux, Jona Lelmi. 2021-01-27. De Giorgi's inequality for the thresholding scheme with arbitrary mobilities and surface tensions. https://arxiv.org/abs/2101.11663

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