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...
L'equazione di Perona-Malik e' stata introdotta ormai vent'anni or sono nel contesto del trattamento d'immagini. Nella sua versione semplificata in dimensione uno si tratta di un'equazione parabolica ...
In this talk, I will show how Machine Learning can help solving the well-known Shape-from-shading problem. This problem is usually solved using either methods of resolution of the PDEs or optimization...
Prenderemo in considerazione alcune equazioni ellittiche frazionarie ed alcuni problemi geometrici a loro collegati, tra cui: simmetria e rigidita` delle soluzioni, stime di densita`, Gamma-convergenz...
Data una varietà Riemanniana compatta, regolare, di dimensione finita n, senza frontiera, possiamo dimostrare che, per una generica metrica g, tutti i punti critici della curvatura scalare S_g associa...
We present some of the results obtained in collaboration with Boccardo, Leonori and Porretta about the existence of positive solutions of Dirichlet problems like \begin{equation} \left\{ \begin{array}...
Usually, least action principles lead to hamiltonian, conservative and time reversible solutions in which no dissipation effect can be input. We show, through some examples related to ODEs or PDEs in ...
I will present joint results with H.-M. Nguyen concerning the study of the Jacobian determinant of maps from R^N into R^N (and also S^N into S^N). New estimates in the Wasserstein metric illuminate cl...
On a compact Riemannian manifold, we present stability results and their instability counterpart for sign-changing solutions of elliptic equations with critical nonlinearities. Such equations are said...
We will discuss the relationships of the Monge problem with a common differential model in granular matter theory. We will show that the Monge problem permits to prove existence and uniqueness/multipl...
In this talk, we introduce a fast multilevel method for solving minimization problems arising in various image restoration problems. Different from traditional multilevel methods which solve the the m...
