图 书 馆
高达维数9的双线性椭圆型方程的稳定解是光滑的Stable solutions to semilinear elliptic equations are smooth up to dimension 9 |
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| 课程网址: | https://videolectures.net/8ecm2021_cabre_stable_solutions/ |
| 主讲教师: | Xavier Cabré |
| 开课单位: | 8ECM会议 |
| 开课时间: | 2021-07-06 |
| 课程语种: | 英语 |
| 中文简介: |  |
| 课程简介: | The regularity of stable solutions to semilinear elliptic PDEs has been studied since the 1970’s. In dimensions 10 and higher, there exist stable energy solutions which are singular. In this talk I will describe a recent work in collaboration with Figalli, Ros-Oton, and Serra, where we prove that stable solutions are smooth up to the optimal dimension 9. This answers to an open problem posed by Brezis in the mid-nineties concerning the regularity of extremal solutions to Gelfand-type problems. |
| 关 键 词: | 高达维数9; 椭圆型方程; 稳定解 |
| 课程来源: | 视频讲座网 |
| 数据采集: | 2024-05-28：liyq |
| 最后编审: | 2024-05-28：liyq |
| 阅读次数: | 5 |