## 偏微分方程式セミナー(2017/10/20): Critical and subcritical fractional Trudinger-Moser type inequalities on $\mathbb{R}$，高橋 太 氏 (大阪市立大学)

2017年 　 10月 20日 16時 30分 ～ 2017年 　 10月 20日 17時 30分

In this talk, we concern with the critical and subcritical Trudinger-Moser type inequalities for functions in a fractional Sobolev space $H^{1/2,2}$ on the whole real line. We introduce Li-Ruf (LR) type and Adachi-Tanaka (AT) type Trudinger-Moser inequalities and study their best constants. We prove the validity of the Adachi-Tanaka type inequality for all expected values of exponents, and the existence of the maximizers for the corresponding supremum. Also we show that a relation between supremums of AT-type and LR-type. This talk is based on a preprint (to appear in Adv. Nonlin. Anal.).