A Trudinger-Moser inequality for a conical metric in the unit ball (Q2414680)

The authors prove Trudinger-Moser inequalities for a conical metric in the unit ball of the Euclidean space \(\mathbb{R}^N\) (\(N \geqslant 2\)); moreover, extremal functions for such inequalities are shown to exist. The results generalize previous inequalities due to \textit{Adimurthi} and \textit{K. Sandeep} [NoDEA, Nonlinear Differ. Equ. Appl. 13, No. 5--6, 585--603 (2007; Zbl 1171.35367)] and \textit{D. G. de Figueiredo} et al. [Proc. Am. Math. Soc. 144, No. 8, 3369--3380 (2016; Zbl 1341.35080)].