Local $C^{1,\beta }$-regularity at the boundary of two dimensional sliding almost minimal sets in $\mathbb {R}^{3}$
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- by Yangqin Fang HTML | PDF
- Trans. Amer. Math. Soc. Ser. B 8 (2021), 130-189
Abstract:
In this paper, we will give a $C^{1,\beta }$-regularity result on the boundary for two dimensional sliding almost minimal sets in $\mathbb {R}^3$. This effect may apply to the regularity of the soap films at the boundary, and may also lead to the existence of a solution to the Plateau problem with sliding boundary conditions proposed by Guy David in the case that the boundary is a 2-dimensional smooth submanifold.References
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Additional Information
- Yangqin Fang
- Affiliation: School of Mathematics and Statistics, Huazhong University of Science and Technology, 430074, Wuhan, People’s Republic of China
- MR Author ID: 1206582
- Email: yangqinfang@hust.edu.cn
- Received by editor(s): July 6, 2018
- Received by editor(s) in revised form: January 29, 2019, April 10, 2019, and April 11, 2019
- Published electronically: February 25, 2021
- Additional Notes: The author was supported in part by the National Natural Science Foundation of China under Grant 11801198, in part by the Fundamental Research Funds for the Central Universities under Grant 2018KFYYXJJ039, in part by the National Natural Science Foundation of China under Grant 11871090.
- © Copyright 2021 by the author under Creative Commons Attribution-Noncommercial 3.0 License (CC BY NC 3.0)
- Journal: Trans. Amer. Math. Soc. Ser. B 8 (2021), 130-189
- MSC (2020): Primary 49K99, 49Q20, 49J99
- DOI: https://doi.org/10.1090/btran/40
- MathSciNet review: 4220652