このアイテムのアクセス数: 41
このアイテムのファイル:
| ファイル | 記述 | サイズ | フォーマット | |
|---|---|---|---|---|
| s00205-023-01881-w.pdf | 803 kB | Adobe PDF | 見る/開く |
| タイトル: | The Existence of a Weak Solution to Volume Preserving Mean Curvature Flow in Higher Dimensions |
| 著者: | Takasao, Keisuke    https://orcid.org/0000-0003-3837-6364 (unconfirmed) |
| 著者名の別形: | 髙棹, 圭介 |
| 発行日: | Jun-2023 |
| 出版者: | Springer Nature |
| 誌名: | Archive for Rational Mechanics and Analysis |
| 巻: | 247 |
| 号: | 3 |
| 論文番号: | 52 |
| 抄録: | In this paper, we construct a family of integral varifolds, which is a global weak solution to the volume preserving mean curvature flow in the sense of $$L^2$$-flow. This flow is also a distributional BV-solution for a short time, when the perimeter of the initial data is sufficiently close to that of a ball with the same volume. To construct the flow, we use the Allen–Cahn equation with a non-local term motivated by studies of Mugnai, Seis, and Spadaro, and Kim and Kwon. We prove the convergence of the solution for the Allen–Cahn equation to the family of integral varifolds with only natural assumptions for the initial data. |
| 著作権等: | © The Author(s) (2023) This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. |
| URI: | http://hdl.handle.net/2433/284485 |
| DOI(出版社版): | 10.1007/s00205-023-01881-w |
| 出現コレクション: | 学術雑誌掲載論文等 |
このアイテムは次のライセンスが設定されています: クリエイティブ・コモンズ・ライセンス
