A trace Trudinger-Moser inequality involving 𝐿^{𝑝}-norm on a compact Riemann surface with boundary

Abstract

In this paper, using the method of blow-up analysis, we establish a trace Trudinger-Moser inequality involving L p L^p -norm and obtain the corresponding extremal on a compact Riemann surface with a smooth boundary. The result generalizes those of Li-Liu [Math. Z. 250 (2005), pp. 363–686] and Zhang [Commun. Pure Appl. Anal. 20 (2021), pp. 1721–1735].