PDE Seminar (2017/10/20): Critical and subcritical fractional Trudinger-Moser type inequalities on $\mathbb{R}$, Futoshi Takahashi (Osaka City University)

2017-10-20 16:30 - 2017-10-20 17:30
Faculty of Science Building #3, Room 309
Futoshi Takahashi (Osaka City University)
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.).