9 jul 2019 -- 14:00
Aula Mancini, SNS, Pisa
Abstract.
This talk is concerned with a Liouville mean field problem on compact surfaces. The interest of this type of equations is motivated by some problems which arise in Differential Geometry and Physics. We will focus on the case of surfaces with boundary and we will impose a particular Neumann boundary condition. We give some results on the solvability of the problem using variational techniques, including a new Moser-Trudinger type inequality. In order to do it, we deal with the possible blow--up phenomenon and we establish a general criterion. Joint work with Luca Battaglia (Università di Roma Tre).