| Singular Supercritical Trudinger–Moser Inequalities and the Existence of Extremals |
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| 基金项目： | Supported by NSFC (Grant No. 11901031) and Beijing Institute of Technology Research Fund Program for Young Scholars (Grant No. 3170012221903) |
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| 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.
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Singular Supercritical Trudinger-Moser Inequalities and the Existence of Extremals |
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| Authors: | Xu Min WANG |
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| Institution: | School of Mathematical Sciences, Beijing Normal University, Beijing 100875, P. R. China |
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| 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. |
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| Keywords: | Singular supercritical Trudinger-Moser inequality radial lemma concentrationcompactness principle extremal functions |
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