A Moser-Trudinger Inequality for the Singular Toda System
by Luca Battaglia   Andrea Malchiodi  

Vol. 9 No. 1 (2014) P.1~P.23

ABSTRACT

In this paper we prove a sharp version of the Moser-Trudinger inequality for the Euler-Lagrange functional of a singular Toda system, motivated by the study of models in Chern-Simons theory. Our result extends those in [14] and [37] for the scalar case, as well as that in [23] for the regular Toda system. We expect this inequality to be a basic tool to attack variationally the existence problem under general assumptions.

KEYWORDS
Toda system, best constants, Moser-Trudinger inequalities, singular Liouville equations

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 35J50, 35J61, 35R01

MILESTONES

Received: 2013-07-15
Revised : 2013-10-04
Accepted: 2013-10-04

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