01019nas a2200121 4500008004100000245008500041210006900126260001000195520053500205653002000740100002200760856011500782 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://www.math.sissa.it/publication/sharp-inequalities-and-blow-analysis-singular-moser-trudinger-embeddings00685nas a2200097 4500008004100000245008200041210006900123520032200192100002200514856005100536 2015 en d00aSingular Liouville Equations on S^2: Sharp Inequalities and Existence Results0 aSingular Liouville Equations on S2 Sharp Inequalities and Existe3 aWe prove a sharp Onofri-type inequality and non-existence of extremals for a Moser-Tudinger functional on S^2 in the presence of potentials having positive order singularities. We also investigate the existence of critical points and give some sufficient conditions under symmetry or nondegeneracy assumptions.

1 aMancini, Gabriele uhttp://urania.sissa.it/xmlui/handle/1963/34489