论文标题
在Adimurthi-Druet类型和极端功能的急剧不平等上
On a sharp inequality of Adimurthi-Druet type and extremal functions
论文作者
论文摘要
本文我们的主要目的是确定对整个空间上分数维度的Adimurthi-Druet类型急剧不平等的极端功能的存在和不存在。确切地说，在整个空间中，我们将尖锐的Trudinger-Moser类型不等式扩展为（calc.var.var.partial微分方程，\ textbf {52}（2015）125-163）。此外，我们执行Carleson-Chang的两步策略一起炸毁分析方法，以确保对亚临界和关键制度的相关极端问题的最大化剂存在。在某些特殊情况下，我们还根据次临界制度提出了不存在的结果。
Our main purpose in this paper is to establish the existence and nonexistence of extremal functions for sharp inequality of Adimurthi-Druet type for fractional dimensions on the entire space. Precisely, we extend the sharp Trudinger-Moser type inequality in (Calc.Var.Partial Differential Equations, \textbf{52} (2015) 125-163) for the entire space. In addition, we perform the two-step strategy of Carleson-Chang together blow up analysis method to ensure the existence of maximizers for the associated extremal problems for both subcritical and critical regimes. We also present a nonexistence result under subcritical regime for some special cases.
