Extremal functions for Trudinger-Moser inequalities of Adimurthi-Druet type in dimension two

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:258

Article

Yang, Yunyan

关键词: Extremal function;    Trudinger-Moser inequality;    Blow-up analysis;   

DOI  :  10.1016/j.jde.2015.01.004

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

Free