https://neckpinch.com/authors/christoph-hurm/New arXiv papers by Christoph Hurm, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2410.08596/arxiv:2410.08596Fri, 11 Oct 2024 00:00:00 GMTHelmut Abels, Christoph Hurm, Maximilian Moser — 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 L²-estimate for the difference of the nonlocal operator and the negative Laplacian from Abels, Hurm arXiv:2307.02264. To this end, we prove a nonlocal Ehrling-type inequality to show uniform H³-estimates for the nonlocal solutions.Mean curvature flowBoundaries & non-compactEigenvalues & spectrumPhase fields & multiphase flows