@article {2015, title = {A note on compactness properties of the singular Toda system}, journal = {Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. }, volume = {26}, number = {Rendiconti Lincei. Mathematics and Applications;vol. 26, Issue 3}, year = {2015}, pages = {299-307}, abstract = {

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.

}, doi = {10.4171/RLM/708}, author = {Luca Battaglia and Gabriele Mancini} } @article {2015, title = {Onofri-Type Inequalities for Singular Liouville Equations}, year = {2015}, publisher = {Springer US}, abstract = {

We study the blow-up behavior of minimizing sequences for the singular Moser{\textendash}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.

}, doi = {10.1007/s12220-015-9589-3}, author = {Gabriele Mancini} } @mastersthesis {2015, title = {Sharp Inequalities and Blow-up Analysis for Singular Moser-Trudinger Embeddings.}, year = {2015}, school = {SISSA}, abstract = {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.}, keywords = {Moser-Trudinger}, author = {Gabriele Mancini} } @article {2015, title = {Singular Liouville Equations on S^2: Sharp Inequalities and Existence Results}, year = {2015}, abstract = {

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.

}, url = {http://urania.sissa.it/xmlui/handle/1963/34489}, author = {Gabriele Mancini} } @article {11613, title = {Remarks on the Moser{\textendash}Trudinger inequality}, journal = {Advances in Nonlinear Analysis}, volume = {2}, number = {Advances in nonlinear analysis;volume 2; issue 4}, year = {2013}, note = {The article is composed of 32 pages inad recorded in PDF format}, pages = {389-425}, publisher = {Advances in Nonlinear Analysis}, abstract = {

We extend the Moser-Trudinger inequality to any Euclidean domain satisfying Poincar{\'e}{\textquoteright}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.

}, doi = {10.1515/anona-2013-0014}, url = {http://edoc.unibas.ch/43974/}, author = {Gabriele Mancini and Luca Battaglia} }