Moser–Trudinger trace inequalities on a compact Riemannian surface with boundary

Yunyan Yang

Vol. 227 (2006), No. 1, 177–200

DOI: 10.2140/pjm.2006.227.177

Abstract

Let $\left(M,g\right)$ 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 $\left(M,g\right)$.

Keywords

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

Mathematical Subject Classification 2000

Primary: 58J05, 58J32

Milestones

Received: 26 November 2004

Revised: 27 January 2005

Accepted: 15 February 2005

Published: 1 September 2006