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...
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...
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...
Le dislocazioni sono uno dei difetti piu' comuni dei solidi cristallini e la loro presenza influenza il comportamento dei materiali in svariati modi. Per esempio, nell'elettronica dei semiconduttori l...
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 ...
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 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 ...
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...
We present short time existence, uniqueness, and regularity results for a surface diffusion evolution equation with curvature regularization in the context of epitaxially strained two-dimensional film...
Baouendi-Grushin operators are important classes of degenerate elliptic operators which are strongly connected with other domains of mathematics such as subriemannian geometry. Parabolic problems asso...
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...
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...
