We discuss the dynamical behavior of the semiflow associated to the nonlinear heat equation ut − ∆u = f(x, u) on a bounded domain with Dirichlet boundary conditions. The nonlinearity f grows superline...
We consider travelling waves in spatially recurrent diffusive media, including the almost periodic and quasi-periodic ones as special cases. We first define the notion of travelling waves under such h...
We study the asymptotic behaviour near the boundary of explosive solutions of a viscous Hamilton-Jacobi equation. This model was introduced by J.M. Lasry and P.L. Lions from a state constrained proble...
Lo scopo del seminario e di presentare alcuni recenti risultati riguardanti le soluzioni dell’equazione di Lane-Emden in domini non limitati dello spazio euclideo ad N dimensioni. In particolare, si p...
Nell’ambito dei funzionali integrali del calcolo delle variazioni, stime puntuali per i minimi sono ben note nel caso scalare. Nel caso vettoriale, il controesempio di De Giorgi pone forti vincoli. No...
I will present some recent joint work with C. Arezzo and M. Singer concerning the existence of extremal metrics in Kahler geometry. The problem reduces to some perturbation result for some fouth order...
I will discuss some recent results on the existence of multiple solutions to equations of the form −∆u = f(x, u), where the nonlinearity f has subcritical or critical growth. In some cases we find sig...
In this talk, will be presented some results on the optimal constants of Sobolev and Hardy-Sobolev inequalities with weights and their relation with the behavior of some mixed Dirichlet-Neumann bounda...
We will review smoothing problems for dispersive equations, in particular for the Schrodinger equation. We will relate these problems to the global analysis of certain Fourier integrals, spectral prob...
