图 书 馆
从极小表面的分支奇点到冰-水界面的非光滑点From branching singularities of minimal surfaces to non-smoothness points on an ice-water interface |
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| 课程网址: | https://videolectures.net/videos/8ecm2021_serra_from_branching |
| 主讲教师: | Joaquim Serra |
| 开课单位: | 信息不详。欢迎您在右侧留言补充。 |
| 开课时间: | 2021-07-06 |
| 课程语种: | 英语 |
| 中文简介: |  |
| 课程简介: | Stefan’s problem, dating back to the XIX century, aims to describe the evolution of a block of ice melting in water. Its mathematical analysis experienced few progress until the 1970’s, when Duvaut reformulated it as the gradient flow of a nice convex functional. In 1977, Caffarelli proved that the ice-water interface is an smooth surface outside of a certain closed set: the so-called singular set. This was as huge breakthrough. However, methods available back in the 1970’s did not allow for a fine description of the structure of the singular set. During the following 20 years, Almgren developed his theory of branching singularities of minimal surfaces, and in 2008 these methods were applied to the not-so-well-known “thin obstacle problem”. This induced, in recent years, a fruitful use of Almgren’s methods to study singularities in Stefan’s problem. But even with these powerful new tools in hand, we were only halfway to obtaining a fully satisfying description of the non-smoothness points on an ice-water interface |
| 关 键 词: | 梯度流; 冰水界面; 奇异集 |
| 课程来源: | 英国开放大学 |
| 数据采集: | 2025-01-25：zsp |
| 最后编审: | 2025-02-26：zsp |
| 阅读次数: | 4 |