%0 Journal Article %J Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. %D 2015 %T A note on compactness properties of the singular Toda system %A Luca Battaglia %A Gabriele Mancini %X

In this note, we consider blow-up for solutions of the SU(3) Toda system on compact surfaces. In particular, we give a complete proof of a compactness result stated by Jost, Lin and Wang and we extend it to the case of singular systems. This is a necessary tool to find solutions through variational methods.

%B Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. %V 26 %P 299-307 %G en %1 34669 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by gmancini@sissa.it (gmancini@sissa.it) on 2015-08-07T16:01:01Z No. of bitstreams: 1 art3.pdf: 146803 bytes, checksum: 362923e2dd63f86658dd3bb0701ce05b (MD5) %R 10.4171/RLM/708 %0 Journal Article %D 2015 %T Onofri-Type Inequalities for Singular Liouville Equations %A Gabriele Mancini %X

We study the blow-up behavior of minimizing sequences for the singular Moser–Trudinger functional on compact surfaces. Assuming non-existence of minimum points, we give an estimate for the infimum value of the functional. This result can be applied to give sharp Onofri-type inequalities on the sphere in the presence of at most two singularities.

%I Springer US %G en %1 34668 %2 Mathematics %4 1 %# MAT/05 %R 10.1007/s12220-015-9589-3 %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) %0 Journal Article %J Advances in Nonlinear Analysis %D 2013 %T Remarks on the Moser–Trudinger inequality %A Gabriele Mancini %A Luca Battaglia %X

We extend the Moser-Trudinger inequality to any Euclidean domain satisfying Poincaré's inequality. We find out that the same equivalence does not hold in general for conformal metrics on the unit ball, showing counterexamples. We also study the existence of extremals for the Moser-Trudinger inequalities for unbounded domains, proving it for the infinite planar strip.

%B Advances in Nonlinear Analysis %I Advances in Nonlinear Analysis %V 2 %P 389-425 %G en %U http://edoc.unibas.ch/43974/ %N 4 %1 34666 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by gmancini@sissa.it (gmancini@sissa.it) on 2015-08-07T13:45:19Z No. of bitstreams: 1 articolo1.pdf: 526978 bytes, checksum: 941a2e14ae2d0ff88b198a2e8c8c153e (MD5) %R 10.1515/anona-2013-0014