%0 Thesis %D 2015 %T Sharp Inequalities and Blow-up Analysis for Singular Moser-Trudinger Embeddings. %A Gabriele Mancini %K Moser-Trudinger %X We 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. %I SISSA %G en %1 34738 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by gmancini@sissa.it (gmancini@sissa.it) on 2015-09-22T12:27:17Z No. of bitstreams: 1 tesi4.pdf: 1376221 bytes, checksum: cfc85996d91a3384e94546a64bf8c479 (MD5) %0 Report %D 2015 %T Singular Liouville Equations on S^2: Sharp Inequalities and Existence Results %A Gabriele Mancini %X

We 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.

%G en %U http://urania.sissa.it/xmlui/handle/1963/34489 %1 34672 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by gmancini@sissa.it (gmancini@sissa.it) on 2015-08-11T09:06:30Z No. of bitstreams: 1 art4.pdf: 352978 bytes, checksum: 4e081003a6b037544c46954c3d44b826 (MD5)