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...
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...
The asymptotic behavior of the solutions of an elliptic Dirichlet linear problem, where the coefficients vary periodically has been considered by several authors. However, the classical approximation ...
I review the connection between semilinear elliptic equations and their numerical aproximation. In particular, I consider how a recent counterexample of Souplet extends to regions with corners, and th...
Based on Griffith’s criterion for crack growth, a method was proposed for determining crack paths by taking continuous-time limits of discrete-time variational problems. This has been successfully car...
We extende the resolution of the Yamabe conjecture to the Cauchy-Riemann manifolds and precisely the case left open by D. Jenson and J. Lee: the conformally flat case and the case n = 1, where 2n + 1 ...
The Mountain Pass Theorem is an important tool in the calculus of variations and in finding solutions to nonlinear PDEs in general. It is important not only for the theory but since publishing the Mou...
I will present briefly the mathematical models describing a dilute Bose gas. Then, explain the Bose condensation from a simple mathematical point of view and give the model describing the system dilut...
We consider the movement of the set of maximum points of the solution of the heat equation in the exterior domain of a ball, under the Neumann boundary condition. We prove that the set of the maximum ...
In questo seminario discutero' una classe di problemi ellittici in domini regolari con campi di trasporto singolari alla frontiera, es. dell'ordine dell'inverso della distanza al bordo. L'interesse pe...
