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

Zhang, Mengjie

doi:10.1090/proc/16750

A trace Trudinger-Moser inequality involving $L^p$-norm on a compact Riemann surface with boundary
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by Mengjie Zhang;

Proc. Amer. Math. Soc. 152 (2024), 2555-2570

DOI: https://doi.org/10.1090/proc/16750

Published electronically: April 18, 2024

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Abstract:

In this paper, using the method of blow-up analysis, we establish a trace Trudinger-Moser inequality involving $L^p$-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].

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