@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 = {

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.

}, issn = {1432-1823}, doi = {10.1007/s00209-015-1584-7}, url = {https://doi.org/10.1007/s00209-015-1584-7}, author = {Luca Battaglia} } @article {battaglia2013moser, title = {A Moser-Trudinger inequality for the singular Toda system}, journal = {Bull. Inst. Math. Acad. Sin.}, volume = {9}, number = {1}, year = {2014}, pages = {1{\textendash}23}, author = {Luca Battaglia and Andrea Malchiodi} }