01015nas a2200121   4500008004100000245008500041210006900126260001000195520053500205653002000740100002200760856011100782       2015                        en  d00aSharp Inequalities and Blow-up Analysis for Singular Moser-Trudinger Embeddings.0 aSharp Inequalities and Blowup Analysis for Singular MoserTruding  bSISSA3 aWe investigate existence of solutions for a singular Liouville equation on S^2 and prove sharp Onofri-type inequalities for a Moser-Trudinger functional in the presence of singular potentials. As a consequence we obtain existence of extremal functions for the Moser-Trudinger embedding on compact surfaces with conical singularities. Finally we study the blow-up behavior for sequences of solutions Liouville-type systems and prove a compactness condition which plays an important role in the variational analysis of Toda systems.10aMoser-Trudinger1 aMancini, Gabriele  uhttps://math.sissa.it/publication/sharp-inequalities-and-blow-analysis-singular-moser-trudinger-embeddings