Mathematics

We present a class of variational equations with exponential nonlinearities on a compact Riemannian surface, describing the mean field equation of the equilibrium turbulance with arbitrarily signed vortices. We consider the problem with supercritical parameters and we give an existence result by using variational methods. In doing this, we present a new Moser-Trudinger type inequality under suitable conditions on the center of mass and the scale of concentration of the function involved in the equation.

This seminar is part of the AJS series of seminars.