On the bounds of sharp Trudinger-Moser inequalities

Hanli Tang

In this paper, we establish the bounds of sharp Trudinger-Moser inequalities on Euclidean space. Let $B$ be a ball in ${\mathbb{R}}^n$ and $$TM(B)=\sup_{u\in{W_{0}^{1,n}(B)},\|\nabla…