TY - JOUR T1 - Moser–Trudinger inequalities for singular Liouville systems JF - Mathematische Zeitschrift Y1 - 2016 A1 - Luca Battaglia AB -

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.

VL - 282 UR - https://doi.org/10.1007/s00209-015-1584-7 ER -