We consider the evolution of an interface generated between two immiscible, incompressible and irrotational fluids. Specifically we study the Muskat equation (the interface between oil and water in sa...
The limit behaviour of variational systems depending on small parameters (e.g. homogenization, phase transitions, etc.) is often successfully described in terms of Gamma-convergence both in the static...
I will first give two (similar) ways for proving the existence of a weak solution for the compressible (stationary) stokes problem : passing to the limit using (in particular) a viscous approximation ...
The classical Faber-Krahn inequality asserts that balls (uniquely) minimize the first eigenvalue of the Dirichlet-Laplacian among sets with given volume. I will show a sharp quantitative enhancement o...
I will study a nonlinear heat equation with a periodic timeoscillating term in factor of the nonlinearity. In particular, I will give examples showing how the behavior of the solution can drastically ...
Lower curvature bounds play an important role in the study of singular spaces. In 2005 Lott, Sturm and Villani presented a synthetic definition in terms of Optimal Transportation of a metric space end...
In questo seminario discuterò alcuni risultati ottenuti in collaborazione con Vladimir Maz'ya. Questi riguardano la dissipatività negli spazi L^{p} (1 < p < +\infty ), degli operatori differenzi...
In un recente lavoro, Ambrosio, Frid e Silva studiano un problema di omogeneizzazione per una classe di equazioni di tipo porous medium in cui la funzione flusso è un processo stocastico stazionario s...
Given a Borel A in \mathbb{R}^n of positive measure, one can consider its semisum S=(A+A)/2. It is clear that S contains A, and it is not difficult to prove that they have the same measure if and only...
In this talk, I will discuss some questions related to the nonlinear theory of electromagnetism formulated by Born and Infeld in 1934. I will discuss the link between this theory and the curvature ope...
