Abstract

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).

Keywords

Moser–Trudinger inequality, trace imbedding theorem, blowing-up analysis, extremal functions

Mathematical Subject Classification

Primary: 58J05, 58J32

Authors