De Giorgi's inequality for the thresholding scheme with arbitrary mobilities and surface tensions
Analysis of PDEs
2021-01-29 v1
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.
Keywords
Cite
@article{arxiv.2101.11663,
title = {De Giorgi's inequality for the thresholding scheme with arbitrary mobilities and surface tensions},
author = {Tim Laux and Jona Lelmi},
journal= {arXiv preprint arXiv:2101.11663},
year = {2021}
}