| Remarks on the Extremal Functions for the Moser-Trudinger Inequality |
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| 引用本文： | Yu Xiang LI（Yuxiang LI）. Remarks on the Extremal Functions for the Moser-Trudinger Inequality[J]. 数学学报(英文版), 2006, 22(2): 545-550. DOI: 10.1007/s10114-005-0568-7 |
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| 作者姓名： | Yu Xiang LI（Yuxiang LI） |
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| 作者单位： | Department of Mathematical Science, Tsinghua University, Beijing 100084, P. R. China |
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| 摘 要： | We will show in this paper that if A is very close to 1, thenI（M,λ,m） =supu∈H0^1,n（m）,∫m｜△↓u｜^ndV=1∫Ω（e^αn｜u｜^n/（n-1）-λm∑k=1｜αnun/（n-1）｜k/k!）dVcan be attained, where M is a compact-manifold with boundary. This result gives a counter-example to the conjecture of de Figueiredo and Ruf in their paper titled ＂On an inequality by Trudinger and Moser and related elliptic equations＂ （Comm. Pure. Appl. Math., 55, 135-152, 2002）.
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| 关 键 词： | Moser-Trudinger不等式 极值函数 紧密流程 边界值 |
| 收稿时间： | 2003-06-25 |
| 修稿时间： | 2003-06-252003-12-24 |
Remarks on the Extremal Functions forthe Moser–Trudinger Inequality |
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| Yu Xiang Li. Remarks on the Extremal Functions forthe Moser–Trudinger Inequality[J]. Acta Mathematica Sinica(English Series), 2006, 22(2): 545-550. DOI: 10.1007/s10114-005-0568-7 |
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| Authors: | Yu Xiang Li |
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| Abstract: | We will show in this paper that if λ is very close to 1, then can be attained, where M is a compact–manifold with boundary. This result gives a counter–example to the conjecture of de Figueiredo and Ruf in their paper titled "On an inequality by Trudinger and Moser and related elliptic equations" (Comm. Pure. Appl. Math., 55, 135–152, 2002). |
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| Keywords: | Moser-Trudinger inequality extremal function |
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