Moser–Trudinger inequalities for singular Liouville systems

Battaglia, Luca
(2015) Mathematische Zeitschrift — Vol. 282, n° 3-4, p. 1169-1190 (2015)

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  • Battaglia, LucaUCLouvain
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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 energyminimizing 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.
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Battaglia, L. (2015). Moser–Trudinger inequalities for singular Liouville systems. Mathematische Zeitschrift, 282(3-4), 1169-1190. https://doi.org/10.1007/s00209-015-1584-7 (Original work published 2015)