A sharp Trudinger-Moser type inequality for unbounded domains in ${\mathbb{R}}^n$

Yuxiang Li, Bernhard Ruf

The Trudinger-Moser inequality states that for functions $u\in H_0^{1,n}(\Omega )$ ($\Omega \subset {\mathbb{R}}^n$ a bounded domain) with ${\int }_{\Omega }|\nabla u{|}^{n}dx\le 1$ one has $\int_Ω(e^{α_n|u|^…