Consideriamo un'equazione di Liouville su superfici compatte motivata dallo studio di modelli di Chern-Simons autoduali e dal problema di prescrizione della curvatura Gaussiana con singolarità coniche...
We consider extremum problems for some classical functionals of the Calculus of Variations (such as torsional rigidity, first Dirichlet eigenvalue, electrostatic capacity), subject to geometric constr...
If \phi:R\to R is a non-convex energy density, the initial-boundary value problem for the equation (1) \begin{equation} \left\{ \begin{array}{ll} u_t+\frac{1}{2}(\phi(u_x))_x,x\in(0,1) \\ u(\cdot,0)=u...
Equazioni alle derivate parziali su grafi hanno numerose applicazioni (per esempio modelli di traffico, circolazione del sangue, social networks, internet, etc.). In molti di questi problemi e' import...
We describe some recent work on the semiclassical limit of the linear Schrodinger equation. Under mild regularity assumptions on the potential U which include Born-Oppenheimer potential energy surface...
Given a vector homogeneous differential operator of order 1 A(D) acting on vector fields, I will answer to the question whether there is a Gagliardo--Nirenberg type estimate of the form ||u||_{L^{n/(n...
In this talk we shall present some qualitative results for solutions of the fully nonlinear elliptic Allen Cahn Equation; precisely we shall see that under specific conditions the solutions are one-di...
Dopo aver rivisto alcuni risultati di base e alcuni problemi aperti sul problema isoperimetrico nello spazio Euclideo con densità, discuteremo il caso modello di densità di tipo misto Euclideo-Gaussia...
We prove that any positive solution of \partial_t u-\Delta u+u^q=0 (q>1) in R^N \times (0,\infty) with singular initial trace (F,0), where F is a closed subset of R^N can be represented, up to two ...
In last years, there has been some effort to get quantitative versions of the most classical spectral inequalities, namely the Faber-Krahn inequality for the first eigenvalue of the Dirichlet Laplacia...
