In questo seminario discuteremo il problema isoperimetrico su \mathbb{R}^N dotato di una densità; in altre parole, ci si preoccupa di minimizzare il perimetro a volume fissato, considerando però perim...
Mostriamo che i risultati sull'omogeneizzazione periodica di equazioni di Hamilton-Jacobi possono essere generalizzati sostituendo il toro con una qualsiasi varieta' compatta. Un tale approccio consen...
Given a Tonelli Hamiltonian on a compact manifold, we can construct a compact invariant subset of the cotangent bundle enjoying variational properties which has the distinguished property of being a L...
We will discuss recent works with Duyckaerts and Merle, dealing with global well posedness, blow-up and soliton resolution, for the energy critical wave equation....
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...
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...
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...
