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- W3013780328 abstract "The parabolic Allen-Cahn equation is a semilinear partial differential equation linked to the mean curvature flow by a singular perturbation. We show an improved convergence property of the parabolic Allen-Cahn equation to the mean curvature flow, which is the parabolic analogue of the improved convergence property of the elliptic Allen-Cahn to minimal surfaces by Wang-Wei and Chodosh-Mantoulidis. More precisely, we show if the phase-transition level sets are converging in $C^2$, then they converge in $C^{2,theta}$. As an application, we obtain a curvature estimate for parabolic Allen-Cahn equation, which can be viewed as a diffused version of Brakke's and White's regularity theorem for mean curvature flow" @default.
- W3013780328 created "2020-04-03" @default.
- W3013780328 creator A5053510214 @default.
- W3013780328 date "2020-03-26" @default.
- W3013780328 modified "2023-10-17" @default.
- W3013780328 title "Second order estimates for transition layers and a curvature estimate for the parabolic Allen-Cahn" @default.
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- W3013780328 doi "https://doi.org/10.48550/arxiv.2003.11886" @default.
- W3013780328 hasPublicationYear "2020" @default.
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