We consider maps between spheres \(S^n\) to \(S^\ell\) that minimize the Sobolev-space energy \(W^{s,n/s}\) for some \(s \in (0,1)\) in a given homotopy class. The basic question is: in which homotopy...
We will consider a type of cooperative nonlinear elliptic system in R^N. The interest of this problem is based on the presence of Sobolev or Sobolev-Hardy critical power nonlinearities and a nonlinear...
We consider general two-dimensional autonomous velocity fields and prove that their mixing and dissipation features are limited to algebraic rates. As an application, we consider a standard cellular f...
A classic yet delicate fact of Morse theory states that the unstable manifolds of a Morse-Smale gradient-flow on a closed manifold M are the open cells of a CW-decomposition of M. I will describe a se...
In this talk, we present a general existence result to the problem of prescribing curvatures on a disk under conformal changes of the metric. We treat the case of negative Gaussian curvature, as a fir...
IT: Presenteremo lo stato dell'arte sul problema della regolarità delle curve minime della lunghezza in varietà sub-Riemanniane, un problema aperto da almeno 40 anni. Il seminario avrà un carattere...
We produce complete, non-compact, Riemannian metrics with positive constant \sigma_2-curvature on a sphere of dimension n>4, with a prescribed singular set given by a disjoint union of closed subma...
We study the surface diffusion flow in the flat torus, that is, smooth hypersurfaces moving with the outer normal velocity given by the Laplacian of their mean curvature. This model describes the evol...
In this talk I will discuss some results about long time behaviors of solutions to Hamiltonian PDEs (Schrödinger, Kirchhoff, etc). In particular I will focus on a recent result where we (with J. Berni...
We are interested here in questions related to the maximal regularity of solutions of elliptic problems with Dirichlet boundary condition (see [1]). For the last 40 years, many works have been concern...
