Strong convergence of the thresholding scheme for the mean curvature flow of mean convex sets
| Autor: | Jakob Fuchs, Tim Laux |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Advances in Calculus of Variations. |
| ISSN: | 1864-8266 1864-8258 |
| Popis: | In this work, we analyze Merriman, Bence and Osher's thresholding scheme, a time discretization for mean curvature flow. We restrict to the two-phase setting and mean convex initial conditions. In the sense of the minimizing movements interpretation of Esedoglu and Otto we show the time-integrated energy of the approximation to converge to the time-integrated energy of the limit. As a corollary, the conditional convergence results of Otto and one of the authors become unconditional in the two-phase mean convex case. Our results are general enough to handle the extension of the scheme to anisotropic flows for which a non-negative kernel can be chosen. Comment: 59 pages, 12 figures, revised version, additional examples and discussion |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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