Extremal functions for Trudinger–Moser inequalities with nonnegative weights
Extremal functions for Trudinger–Moser inequalities with nonnegative weights
Using blow-up analysis, the author proves the existence of extremal functions for Trudinger-Moser inequalities with nonnegative weights on bounded Euclidean domains or compact Riemannian surfaces. This extends recent results of Yang (J. Differ. Equ. 258:3161-3193, 2015) and Yang-Zhu (Proc. Am. Math. Soc. 145:3953-3959, 2017).