01034nas a2200145 4500008004100000022001400041245006600055210006600121260000800187300001600195490000800211520060300219100002000822856004600842 2016 eng d a1432-182300aMoser–Trudinger inequalities for singular Liouville systems0 aMoser–Trudinger inequalities for singular Liouville systems cApr a1169–11900 v2823 a
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.
1 aBattaglia, Luca uhttps://doi.org/10.1007/s00209-015-1584-700433nas a2200121 4500008004100000245006200041210005900103300001100162490000600173100002000179700002200199856009000221 2014 eng d00aA Moser-Trudinger inequality for the singular Toda system0 aMoserTrudinger inequality for the singular Toda system a1–230 v91 aBattaglia, Luca1 aMalchiodi, Andrea uhttps://www.math.sissa.it/publication/moser-trudinger-inequality-singular-toda-system