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- W4387030643 abstract "We prove a quantitative convergence result of the nonlocal Allen--Cahn equation to volume-preserving mean curvature flow. The proof uses gradient flow calibrations and the relative entropy method, which has been used in the recent literature to prove weak-strong uniqueness results for mean curvature flow and convergence of the Allen--Cahn equation. A crucial difference in this work is a new notion of gradient flow calibrations. We add a tangential component to the velocity field in order to prove the Gronwall estimate for the relative energy. This allows us to derive the optimal convergence rate without having to show the closeness of the Lagrange-multipliers." @default.
- W4387030643 created "2023-09-26" @default.
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- W4387030643 date "2023-09-21" @default.
- W4387030643 modified "2023-09-27" @default.
- W4387030643 title "Quantitative convergence of the nonlocal Allen--Cahn equation to volume-preserving mean curvature flow" @default.
- W4387030643 doi "https://doi.org/10.48550/arxiv.2309.12409" @default.
- W4387030643 hasPublicationYear "2023" @default.
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