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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...

Si considera l’equazione di reazione-diffusione con potenziale a due pozzi in un intervallo finito con termine forzante aleatorio. Si scelgono condizioni al bordo di Dirichlet non omogenee che impongo...

The problem of Optimal Mass Transport, due to Monge,is to transfer a mass from one location to another trying to minimize a total cost. The case where the cost is the square of the distance on the Euc...

In this lecture I will consider the nonlinear elliptic model problem −div(A(x)∇u(x)) + cu(x) = γ...

Data assimilation problems consist in retrieving the value of the solution at some time (everywhere in the domain) for an evolution problem knowing informations on the solution on a subdomain during a...

Several transport-dffusion systems arise as simple models in chemotaxis (motion of bacterias or amebia interacting through a chemical signal) and in angiogenesis (development of capillary blood vessel...

Si studia il problema di Dirichlet per l’equazione della curvatura media sul disco con dato al bordo gamma. Il problema è variazionale e caratterizzato da mancanza di compattezza. Se la curvatura medi...