Trudinger–Moser-type inequality in weighted spaces

Prof. João Marcos Do Ó
Universidade Federal da Paraíba

Abstract: We deal with an improvement of a Trudinger–Moser-type inequality associated with embedding a class of weighted Sobolev spaces into Orlicz spaces. Our primary purpose in this talk is to present recent results on the existence and nonexistence of extremal functions for sharp Trudinger-Moser inequality of Adimurthi-Druet type for fractional dimensions on the entire space. Precisely, we extend both the improvement of Lions-type and a sharp Trudinger-Moser type inequality for fractional dimensions for the entire space. In addition, we investigate the existence and nonexistence of extremal functions for such as inequalities.