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...
We establish trace Hardy and trace Hardy-Sobolev-Maz'ya inequalities with best Hardy constants, for domains satisfying suitable geometric assumptions such as mean convexity or convexity. We then use t...
We study the motion of discrete interfaces driven by ferromagnetic interactions in a two-dimensional periodic environment, by coupling the minimizing movements approach by Almgren, Taylor and Wang and...
Dislocations are line defects in crystals and they are considered the main mechanism of plastic deformations in metals. We will consider straight dislocations, so that their positions are completely i...
In the study of Hamiltonian systems a special role is played by invariant Lagrangian submanifolds. These objects arise quite naturally in many physical and geometric problems and besides sharing a dee...
