(untitled) (Journal of Partial Differential Equations, 2022)
In this paper, we obtained the extremal function for a weighted singular Trudinger-Moser inequality by blow-up analysis in the Euclidean space R^2. This extends recent results of Hou (J. Inequal. Appl., 2018) and similar result was proved by Zhu (Sci. China Math., 2021).