Extremal functions for Trudinger-Moser inequalities of Adimurthi-Druet type in dimension two
Extremal functions for Trudinger-Moser inequalities of Adimurthi-Druet type in dimension two
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二维 Adimurthi-Druet 型 Trudinger-Moser 不等式的极值函数
DOI：
10.1016/j.jde.2015.01.004
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发表时间：
2015-03-05
影响因子：
2.4
通讯作者：
Yang, Yunyan
中科院分区：
文献类型：
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作者：
Yang, Yunyan
结合Carleson Chang [9]的结果和Blow-up分析，证明了一类二维Trudinger-Moser不等式极值函数的存在性.这类不等式最初是由Adimurthi和O. Druet [1]，作者将其推广到高维情形和黎曼曲面情形[40，41]，C. Tintarev更广泛的情况下，包括单数形式[36]和M。de Souza和J.M.对整个欧氏空间R-2做O [14]。除了欧几里得情形，我们还考虑黎曼曲面情形。本文的结果补充了L. Carleson和A. Chang [9]，M. Struwe [35]，M. Flucher [16]，K. Lin [19]，and Adimurthi and O. [1]，我们以前的[41，26]和C的一部分。Tintarev [36]. (C)2015 Elsevier Inc. All rights reserved.
Combining-Carleson Chang's result [9] with blow-up analysis, we prove existence of extremal functions for certain Trudinger-Moser inequalities in dimension two. This kind of inequality was originally proposed by Adimurthi and O. Druet [1], extended by the author to high dimensional case and Riemannian surface case [40,41], generalized by C. Tintarev to wider cases including singular form [36] and by M. de Souza and J.M. do O [14] to the whole Euclidean space R-2. In addition to the Euclidean case, we also consider the Riemannian surface case. The results in the current paper complement that of L. Carleson and A. Chang [9], M. Struwe [35], M. Flucher [16], K. Lin [19], and Adimurthi and O. Druet [1], our previous ones [41,26], and part of C. Tintarev [36]. (C) 2015 Elsevier Inc. All rights reserved.