Moser–Trudinger trace inequalities on a compact Riemannian surface with boundary
Yunyan Yang · Pacific Journal of Mathematics · 2006
Let (M, g) be a compact smooth Riemannian surface with boundary.In this paper, we use blowing-up analysis to prove that some Moser-Trudinger trace inequalities hold on certain function spaces, and that the extremal functions exist in those function spaces without any additional hypothesis on (M, g).