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This is a Quantitative Study study.

October 11, 2025Asymptotic AnalysisOpen Access

Convergence of the Nonlocal Allen–Cahn Equation to Mean Curvature Flow

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Authors

HAHelmut AbelsUniversity of Regensburg CHChristoph HurmUniversity of Regensburg MMMaximilian MoserInstitute of Science and Technology Austria

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Implication

Analysis shows sharp interface limit of nonlocal allen-cahn equation leads to mean curvature flow, implying new insights for equations in high dimensions.

Key Points

The study finds that the nonlocal allen-cahn equation converges to mean curvature flow under specific conditions.
It reports sharp interface limit analysis with a focus on periodic boundary conditions in two and three dimensions.
The approach combines spectral estimates from the local case with uniform estimates derived from a nonlocal ehrling-type inequality.
It suggests significant implications for the understanding of nonlocal operators and their role in geometric flows.

Cite This Study

Abels et al. (2025) studied this question.

synapsesocial.com/papers/68e9b1d9ba7d64b6fc132df0 https://doi.org/10.1177/09217134251377479

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Implication

Analysis shows sharp interface limit of nonlocal allen-cahn equation leads to mean curvature flow, implying new insights for equations in high dimensions.

Convergence of the Nonlocal Allen–Cahn Equation to Mean Curvature Flow

Discussion

Member takes

Implication

Key Points

Cite This Study

Convergence of the Nonlocal Allen–Cahn Equation to Mean Curvature Flow

Discussion

Member takes

Implication

Key Points

Cite This Study

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