In this talk we will consider a reverse Faber-Krahn inequality for the principal eigenvalue μ_1(Ω) of the fully nonlinear operator P_{+N}u:=λ_N(D2u), where Ω⊂R^N is a bounded, open convex set, and λ_N...
In [Inv. Math., 1978], Morgan proved that almost every curve in R^3 is the boundary of a unique area minimizing surface. I will show how to extend Morgan's result to surfaces of any dimension and codi...
The fact that the flow of a hypersurface by its mean curvature can be seen as a gradient flow of the surface area has motivated an influential minimizing movement scheme (Almgren-Taylor-Wang, Luckhaus...
We address the problem of reconstructing a real potential $V$ from the Dirichlet-to-Neumann map of a Schrödinger operator $-\Delta + V$ on the boundary of a domain in Euclidean space (the reconstructi...
We consider the Euler equations for incompressible fluids in 3-dimension. A classical question that goes back to Helmholtz is to describe the evolution of vorticities with a high concentration around ...
La convergenza in tempo lungo per equazioni di Fokker-Planck con drift confinante è un tema classico, affrontato finora sia con metodi variazionali che probabilistici. Nel seminario discuterò un nuovo...
n this talk we present some results obtained jointly with Matteo Muratori (Politecnico di Milano), focusing on qualitative properties for • Extremals for the Sobolev inequality, • Positive radial solu...
Il moto per curvatura media a volume costante è l'evoluzione di una ipersuperficie con velocità data dalla curvatura media, con un termine aggiuntivo non locale tale che il volume racchiuso resti cost...
I will survey on some long-standing open problems and some recent results about the regularity of minimizers of various relaxed energies. I will focus on the model case of harmonic maps from the 3-dim...
Interfacial energy functionals are ubiquitous in nature. However, some of the most basic questions are still open. In this talk, I will address one of these questions and characterize local minimizers...
