A remark on energy estimates concerning extremals for Trudinger-Moser inequalities on a disc

作者：Yang, Yunyan^*

来源：ARCHIV DER MATHEMATIK, 2018, 111(2): 215-223.

DOI：10.1007/s00013-018-1181-1

• Trudinger-Moser inequality
• Extremal function
• Energy estimate
• Blow-up analysis

In this short note, we generalized an energy estimate due to Malchiodi-Martinazzi (J Eur Math Soc 16:893-908, 2014) and Mancini-Martinazzi (Calc Var 56:94, 2017). As an application, we used it to reprove existence of extremals for Trudinger-Moser inequalities of Adimurthi-Druet type on the unit disc. Such existence problems in general cases had been considered by Yang (Trans Am Math Soc 359:5761-5776, 2007; J Differ Equ 258:3161-3193, 2015) and Lu-Yang (Discrete Contin Dyn Syst 25:963-979, 2009) by using another method.

• 出版日期2018-8
• 单位中国人民大学