A1 Journal article (refereed)
Flat flow solution to the mean curvature flow with volume constraint (2024)
Julin, V. (2024). Flat flow solution to the mean curvature flow with volume constraint. Advances in Calculus of Variations, Early online. https://doi.org/10.1515/acv-2023-0047
JYU authors or editors
Publication details
All authors or editors: Julin, Vesa
Journal or series: Advances in Calculus of Variations
ISSN: 1864-8258
eISSN: 1864-8266
Publication year: 2024
Publication date: 24/04/2024
Volume: Early online
Publisher: Walter de Gruyter GmbH
Publication country: Germany
Publication language: English
DOI: https://doi.org/10.1515/acv-2023-0047
Publication open access: Openly available
Publication channel open access: Partially open access channel
Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/94472
Web address of parallel published publication (pre-print): https://arxiv.org/abs/2301.10089
Abstract
In this paper I will revisit the construction of a global weak solution to the volume preserving mean curvature flow via discrete minimizing movement scheme by Mugnai, Seis and Spadaro [L. Mugnai, C. Seis and E. Spadaro, Global solutions to the volume-preserving mean-curvature flow, Calc. Var. Partial Differential Equations 55 2016, 1, Article ID 18]. This method is based on the gradient flow approach due to Almgren, Taylor and Wang [F. Almgren, J. E. Taylor and L. Wang, Curvature-driven flows: a variational approach, SIAM J. Control Optim. 31 1993, 2, 387–438] and Luckhaus and Sturzenhecker [S. Luckhaus and T. Sturzenhecker, Implicit time discretization for the mean curvature flow equation, Calc. Var. Partial Differential Equations 3 1995, 2, 253–271] and my aim is to replace the volume penalization with the volume constraint directly in the discrete scheme, which from practical point of view is perhaps more natural. A technical novelty is the proof of the density estimate which is based on second variation argument
Keywords: partial differential equations; differential geometry
Free keywords: mean-curvature flow; volume constraint; gradient flow; time discretization
Contributing organizations
Related projects
- Variational problems of isoperimetric type. Stability and Geometric flows (research costs)
- Julin, Vesa
- Research Council of Finland
- Regularity and singularities of geometric evolution equations
- Julin, Vesa
- Research Council of Finland
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