@article {Battaglia2016,
	title = {Moser{\textendash}Trudinger inequalities for singular Liouville systems},
	journal = {Mathematische Zeitschrift},
	volume = {282},
	number = {3},
	year = {2016},
	month = {Apr},
	pages = {1169{\textendash}1190},
	abstract = {<p>In this paper we prove a Moser{\textendash}Trudinger inequality for the Euler{\textendash}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, Poho{\v z}aev-type identities and blow-up analysis.</p>},
	issn = {1432-1823},
	doi = {10.1007/s00209-015-1584-7},
	url = {https://doi.org/10.1007/s00209-015-1584-7},
	author = {Luca Battaglia}
}
