Calculus of Variations and Geometric Measure Theory

T. Laux - J. Lelmi

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

created by lelmi on 03 Feb 2021



Inserted: 3 feb 2021

Year: 2021

ArXiv: 2101.11663 PDF
Links: Arxiv preprint


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─člu 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.