Moser-Trudinger inequalities for singular Liouville systems

TL;DR

This paper establishes a Moser-Trudinger inequality for singular Liouville systems, characterizing parameter conditions for coercivity and providing sharp bounds under specific coefficient assumptions.

Contribution

It introduces a generalized Moser-Trudinger inequality for singular Liouville systems, including parameter characterization and sharp bounds, advancing the understanding of these inequalities.

Findings

Identified parameter ranges for coercivity.

Derived necessary conditions for boundedness.

Established a sharp inequality under coefficient assumptions.

Abstract

In this paper we prove a Moser-Trudinger inequality for the Euler-Lagrange functional of a general singular Liouville system. We characterize the values of the parameters which yield coercivity for the functional and we give necessary conditions for boundedness from below. We also provide a sharp inequality under some assumptions on the coefficients of the system.