A Moser-Trudinger inequality for the singular Toda system

2013/07/15 by Luca Battaglia, Battaglia, Luca, Andrea Malchiodi +1 · 4 citations
Mathematics · Physics and Astronomy · #35J50 #35J61 #35R01 #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Waves and Solitons #math.AP #msc:35J50 #msc:35J61 #msc:35R01

paper · pdf · doi:10.48550/arxiv.1307.3921

13 pages, accepted on Bulletin of the Institute of Mathematica Academia Sinica

openalex publication_date 2013/07/15 · arxiv created 2013/10/07 · arxiv updated 2013/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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