Extremal functions for trace Trudinger-Moser inequalities
Jun Zhang · arXiv (Cornell University) · 2019
In this paper, we concern trace Trudinger-Moser inequalities on a compact Riemann surface with boundary. This kind of inequalities were originally obtained by Liu [19], extended by Li-Liu [16] and Yang [30, 31]. We prove the existence of extremal functions via the method of blow-up analysis. The results in the current paper generalize those of Li-Liu [16] and Yang [32].