Gabriella Zecca

On the existence and blow-up of solutions for a mean field equation with variable intensities

We study an elliptic problem with exponential nonlinearities describing the statistical mechanics equilibrium of point vortices with variable intensities. For suitable values of the physical parameters we exclude the existence of blow-up points on the boundary, we prove a mass quantization property and we apply our analysis to the construction of minimax solutions.

On the Blow-Up of Solutions to Liouville-Type Equations

Abstract We estimate some complex structures related to perturbed Liouville equations defined on a compact Riemannian 2-manifold. As a byproduct, we obtain a quick proof of the mass quantization and we locate the blow-up points.

A multi-species chemotaxis system: Lyapunov functionals, duality, critical mass

This article has been accepted for publication and will appear in a revised form, subsequent to peer review and/or editorial input by Cambridge University Press, in European Journal of Applied Mathematics published by Cambridge University Press. Copyright Cambridge University Press 2017.

An Obstacle Problem for Noncoercive Operators

We study the obstacle problem for second order nonlinear equations whose model appears in the stationary diffusion-convection problem. We assume that the growth coefficient of the convection term lies in the Marcinkiewicz space -.