MENU

You are here

Moser–Trudinger inequalities for singular Liouville systems

TitleMoser–Trudinger inequalities for singular Liouville systems
Publication TypeJournal Article
Year of Publication2016
AuthorsBattaglia, L
JournalMathematische Zeitschrift
Volume282
Pagination1169–1190
Date PublishedApr
ISSN1432-1823
Abstract

In this paper we prove a Moser–Trudinger inequality for the Euler–Lagrange functional of general singular Liouville systems on a compact surface. We characterize the values of the parameters which yield coercivity for the functional, hence the existence of energy-minimizing solutions for the system, and we give necessary conditions for boundedness from below. We also provide a sharp inequality under assuming the coefficients of the system to be non-positive outside the diagonal. The proofs use a concentration-compactness alternative, Pohožaev-type identities and blow-up analysis.

URLhttps://doi.org/10.1007/s00209-015-1584-7
DOI10.1007/s00209-015-1584-7

Sign in