A crucial issue in capillarity-type problems is understanding the behavior of solutions near singular points in the boundary of the container. In the special case of the relative perimeter functional,...
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...
We propose a level set method to reconstruct unknown surfaces from a point cloud, without assuming that the connections between points are known. The formulation of the problem follows the variational...
Numerical simulations often involve 3D objects with spherical topology, e.g. rigid particles, drops, vesicles. When the underlying numerical method is based on boundary integral equations, standard qu...
We review space and time discretizations of the Cahn-Hilliard equation which are energy stable. In many cases, we prove that a solution converges to a steady state as time goes to infinity. The proof ...
