| Singular Supercritical Trudinger–Moser Inequalities and the Existence of Extremals |
| |
| 基金项目： | Supported by NSFC (Grant No. 11901031) and Beijing Institute of Technology Research Fund Program for Young Scholars (Grant No. 3170012221903) |
| |
| 摘 要： | In this paper, we present the singular supercritical Trudinger–Moser inequalities on the unit ball B in R~n, wher~e n ≥ 2. More precisely, we show that for any given α 0 and 0 t n, then the following two inequalities hold for ■,■.We also consider the problem of the sharpness of the constant α_(n,t). Furthermore, by employing the method of estimating the lower bound and using the concentration-compactness principle, we establish the existence of extremals. These results extend the known results when t = 0 to the singular version for 0 t n.
|
Singular Supercritical Trudinger-Moser Inequalities and the Existence of Extremals |
| |
| Xu Min WANG. Singular Supercritical Trudinger-Moser Inequalities and the Existence of Extremals[J]. Acta Mathematica Sinica(English Series), 2020, 36(8): 873-888. DOI: 10.1007/s10114-020-9330-4 |
| |
| Authors: | Xu Min WANG |
| |
| Affiliation: | School of Mathematical Sciences, Beijing Normal University, Beijing 100875, P. R. China |
| |
| Abstract: | In this paper, we present the singular supercritical Trudinger-Moser inequalities on the unit ball B in Rn, where n ≥ 2. More precisely, we show that for any given α > 0 and 0 < t < n, then the following two inequalities hold for ∀ u ∈ W0,r1,n(B),We also consider the problem of the sharpness of the constant αn,t. Furthermore, by employing the method of estimating the lower bound and using the concentration-compactness principle, we establish the existence of extremals. These results extend the known results when t = 0 to the singular version for 0 < t < n. |
| |
| Keywords: | Singular supercritical Trudinger-Moser inequality radial lemma concentrationcompactness principle extremal functions |
| 本文献已被 CNKI 等数据库收录！ |
| 点击此处可从《数学学报(英文版)》浏览原始摘要信息 |
|
点击此处可从《数学学报(英文版)》下载免费的PDF全文 |
