Title | Moser–Trudinger inequalities for singular Liouville systems |
Publication Type | Journal Article |
Year of Publication | 2016 |
Authors | Battaglia, L |
Journal | Mathematische Zeitschrift |
Volume | 282 |
Pagination | 1169–1190 |
Date Published | Apr |
ISSN | 1432-1823 |
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. |
URL | https://doi.org/10.1007/s00209-015-1584-7 |
DOI | 10.1007/s00209-015-1584-7 |
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