Abels, Helmut and Hurm, Christoph and Moser, Maximilian (2025) Convergence of the Nonlocal Allen-Cahn Equation to Mean Curvature Flow. ASYMPTOTIC ANALYSIS. ISSN 0921-7134, 1875-8576
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We prove convergence of the nonlocal Allen-Cahn equation to mean curvature flow in the sharp interface limit, in the situation when the parameter corresponding to the kernel goes to zero fast enough with respect to the diffuse interface thickness. The analysis is done in the case of a W 1 , 1 -kernel, under periodic boundary conditions and in both two and three space dimensions. We use the approximate solution and spectral estimate from the local case, and combine the latter with an L 2 -estimate for the difference of the nonlocal operator and the negative Laplacian from Abels, Hurm Abels, H., & Hurm, C. (2024). Journal of Differential Equations, 402: 593-624. To this end, we prove a nonlocal Ehrling-type inequality to show uniform H 3 -estimates for the nonlocal solutions.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | HILLIARD; nonlocal Allen-Cahn equation; diffuse interface model; sharp interface limit; mean curvature flow |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Helmut Abels |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 21 Apr 2026 05:21 |
| Last Modified: | 21 Apr 2026 05:21 |
| URI: | https://pred.uni-regensburg.de/id/eprint/66081 |
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