A Moser-Trudinger inequality for the singular Toda system

TL;DR

This paper establishes a sharp Moser-Trudinger inequality for the singular Toda system, extending previous results and providing a fundamental tool for analyzing existence problems in related variational models.

Contribution

It introduces a new sharp inequality for the singular Toda system, generalizing known results for scalar and regular Toda cases.

Findings

Proves a sharp Moser-Trudinger inequality for the singular Toda system

Extends previous inequalities from scalar and regular Toda systems

Provides a foundational tool for variational existence proofs

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 for the scalar case, as well as for the regular Toda system. We expect this inequality to be a basic tool to attack variationally the existence problem under general assumptions.