We consider various examples of critical nonlinear partial differential equations which have the following common features: they are Hamiltonian, of dispersive nature, have a conservation law invarian...
Given a Lipschitz vector field, the classical Cauchy-Lipschitz theory gives existence, uniqueness and regularity of the associated ODE flow. In recent years, much attention has been devoted to extensi...
Presenteremo nuovi miglioramenti della disuguaglianza di Sobolev in spazi frazionari tipo H^s in termini di norme di Morrey. Da queste si prova immediatamente esistenza di funzioni ottimali per la dis...
We present some recent results concerning the homogenization of uniformly elliptic equations in nondivergence form. The equations are assumed to have coefficients which are independent at unit distanc...
La teoria dei mean-field games proposta da Lasry e Lions, e in parallelo da Huang, Caines e Malhame', a partire dal 2006, e' un modello di campo medio per dinamiche con grandi popolazioni di piccoli a...
I shall start with a quick review of the basic properties of Steiner symmetrization of sets and functions. Through some recently developed analytical techniques, I will give a characterization of the ...
We study the boundary behaviour of the solutions of (E) \Delta_p u+|\nabla u|^q=0 in a domain \Omega \subset \mathbb R^N, when N\geq p> q>p-1. We first recall the results obtained in the case p=...
In the talk I will describe some nonlinear severly ill-posed inverse boundary value problems involving elliptic equations and elliptic systems with applications to medical imaging, non destructive tes...
In this talk I will discuss some new results on the infinitesimal behavior of 2 dimensional almost minimal surfaces (relevant examples are semi-calibrated currents and section of 3 dimensional minimiz...
Following the method introduced by Evans y Gangbo to solve the classical Monge-Kantorovich mass transport problem, in this lecture we present two mass transport problems obtained as limit when p\to \i...
