Sharp threshold nonlinearity for maximizing the Trudinger-Moser inequalities (Q2334569)

The authors study the existence of a maximizer for the Trudinger-Moser inequality with general non-linearity with critical growth in $\mathbb{R}^2$, as well as in the disk. They also show, in both cases, results of non-existence. The main strategy to prove the main result follows the idea of \textit{L. Carleson} and \textit{S.-Y. A. Chang} [Bull. Sci. Math., II. Sér. 110, 113--127 (1986; Zbl 0619.58013)].